Mckvie - 23-24 April 2018- Pre-training Assessment - 1

1. A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?

Rs 1090

Rs 1160

Rs 1190

Rs 1202

The selling price of the cycle can be found by subtracting the loss from the original price. The loss is calculated by multiplying the original price by the loss percentage (15% of Rs. 1400 = Rs. 210). Subtracting the loss from the original price gives us Rs. 1400 - Rs. 210 = Rs. 1190, which is the selling price of the cycle.

Explanation

The selling price of the cycle can be found by subtracting the loss from the original price. The loss is calculated by multiplying the original price by the loss percentage (15% of Rs. 1400 = Rs. 210). Subtracting the loss from the original price gives us Rs. 1400 - Rs. 210 = Rs. 1190, which is the selling price of the cycle.

2. Select the lettered pair that has the same relationship as Illiterate : Uneducated

Country : State

City : Village

Palace : Hut

Vision : Sight

The correct answer is "Vision : Sight" because just like illiteracy is the state of being uneducated, vision is the state of having sight. Both pairs have a similar relationship where one term represents a state or condition and the other term represents the characteristic or ability associated with that state.

Explanation

The correct answer is "Vision : Sight" because just like illiteracy is the state of being uneducated, vision is the state of having sight. Both pairs have a similar relationship where one term represents a state or condition and the other term represents the characteristic or ability associated with that state.

3. A memory chip has 8 data lines and 9 address lines. How many bytes can be stored on it?

511

512

500

516

A memory chip with 8 data lines can store 2^8 = 256 different combinations of data. Similarly, a memory chip with 9 address lines can address 2^9 = 512 different locations. Since each location can store one byte of data, the memory chip can store a total of 512 bytes.

Explanation

A memory chip with 8 data lines can store 2^8 = 256 different combinations of data. Similarly, a memory chip with 9 address lines can address 2^9 = 512 different locations. Since each location can store one byte of data, the memory chip can store a total of 512 bytes.

4. Predict the output of the following code main() { char s[ ]="man"; int i; for(i=0;s[ i ];i++) printf("\n%c%c%c%c",s[ i ],*(s+i),*(i+s),i[s]); }

Mmm

Mmmmm

Mmmmmm

The code snippet declares a character array `s` with the value "man". It then uses a for loop to iterate through each character of the array. Inside the loop, it uses the `printf` function to print the characters in a specific pattern. The pattern is "%c%c%c%c", where the first `%c` represents the current character `s[i]`, the second `%c` represents the character at the memory location `s+i`, the third `%c` represents the character at the memory location `i+s`, and the fourth `%c` represents the character at the memory location `i[s]`. Since the value of `i` changes in each iteration, the output will be a series of characters based on this pattern. The correct answer "mmmm aaaa nnnn" matches the output of the code.

Explanation

The code snippet declares a character array `s` with the value "man". It then uses a for loop to iterate through each character of the array. Inside the loop, it uses the `printf` function to print the characters in a specific pattern. The pattern is "%c%c%c%c", where the first `%c` represents the current character `s[i]`, the second `%c` represents the character at the memory location `s+i`, the third `%c` represents the character at the memory location `i+s`, and the fourth `%c` represents the character at the memory location `i[s]`. Since the value of `i` changes in each iteration, the output will be a series of characters based on this pattern. The correct answer "mmmm aaaa nnnn" matches the output of the code.

5. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

2:05

3:07

5:03

7:03

The ratio of the first number to the second number is 5:03. This can be determined by setting up an equation based on the given information. Let's assume the first number is x and the second number is y. We are told that 40% of x is equal to two-thirds of y. Mathematically, this can be written as 0.4x = (2/3)y. To find the ratio, we can simplify this equation by multiplying both sides by 10/4, resulting in x = (5/3)y. Therefore, the ratio of the first number to the second number is 5:03.

Explanation

The ratio of the first number to the second number is 5:03. This can be determined by setting up an equation based on the given information. Let's assume the first number is x and the second number is y. We are told that 40% of x is equal to two-thirds of y. Mathematically, this can be written as 0.4x = (2/3)y. To find the ratio, we can simplify this equation by multiplying both sides by 10/4, resulting in x = (5/3)y. Therefore, the ratio of the first number to the second number is 5:03.

6. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

8 , 20 , 28

16 , 28 , 36

20 , 35 , 45

None of These

The present ages of the three persons are in the ratio 4:7:9. Let's assume the ages of the three persons to be 4x, 7x, and 9x respectively.

Eight years ago, their ages would have been (4x-8), (7x-8), and (9x-8) respectively.

According to the given information, the sum of their ages eight years ago was 56.

So, (4x-8) + (7x-8) + (9x-8) = 56.

Simplifying the equation, we get 20x = 80.

Dividing both sides by 20, we find x = 4.

Therefore, the present ages of the three persons are 4x = 16, 7x = 28, and 9x = 36 respectively.

Hence, the correct answer is 16, 28, 36.

Explanation

The present ages of the three persons are in the ratio 4:7:9. Let's assume the ages of the three persons to be 4x, 7x, and 9x respectively.

Eight years ago, their ages would have been (4x-8), (7x-8), and (9x-8) respectively.

According to the given information, the sum of their ages eight years ago was 56.

So, (4x-8) + (7x-8) + (9x-8) = 56.

Simplifying the equation, we get 20x = 80.

Dividing both sides by 20, we find x = 4.

Therefore, the present ages of the three persons are 4x = 16, 7x = 28, and 9x = 36 respectively.

Hence, the correct answer is 16, 28, 36.

7. The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:

1677

1683

2523

3363

To find the least number that satisfies the given conditions, we need to find the least common multiple (LCM) of 5, 6, 7, and 8. The LCM of these numbers is 840. Adding 3 to this number will give us the desired number that leaves a remainder of 3 when divided by 5, 6, 7, and 8. Therefore, the correct answer is 840 + 3 = 843. However, this number does not leave a remainder of 0 when divided by 9. The next multiple of 840 is 1680, which also does not satisfy the condition. The next multiple, 2520, also does not work. Finally, the next multiple, 3360, satisfies the condition as it leaves a remainder of 3 when divided by 5, 6, 7, and 8, and leaves no remainder when divided by 9. Hence, the correct answer is 3360 + 3 = 3363.

Explanation

To find the least number that satisfies the given conditions, we need to find the least common multiple (LCM) of 5, 6, 7, and 8. The LCM of these numbers is 840. Adding 3 to this number will give us the desired number that leaves a remainder of 3 when divided by 5, 6, 7, and 8. Therefore, the correct answer is 840 + 3 = 843. However, this number does not leave a remainder of 0 when divided by 9. The next multiple of 840 is 1680, which also does not satisfy the condition. The next multiple, 2520, also does not work. Finally, the next multiple, 3360, satisfies the condition as it leaves a remainder of 3 when divided by 5, 6, 7, and 8, and leaves no remainder when divided by 9. Hence, the correct answer is 3360 + 3 = 3363.

8. "In this passage, the phrase ""God in man"" implies

God having assumed the shape of man

Neither fully godly nor fully human

Man being transformed into God

The divine qualities in man

The phrase "God in man" implies that there are divine qualities present in man. This suggests that humans have the potential to possess and exhibit godly characteristics or qualities. It does not necessarily mean that God has assumed the shape of man or that man has been transformed into God.

Explanation

The phrase "God in man" implies that there are divine qualities present in man. This suggests that humans have the potential to possess and exhibit godly characteristics or qualities. It does not necessarily mean that God has assumed the shape of man or that man has been transformed into God.

9. According to the author, ""salvation"" of human beings lies in the

Extended trade relations

Spiritual transformation of life

Orgy of national pride

Wholehearted participated in political organisations

The author believes that the "salvation" of human beings lies in the spiritual transformation of life. This suggests that the author believes that true fulfillment and happiness can be achieved through a deep inner change and connection with something greater than oneself. This is in contrast to the other options, which focus on external factors such as trade relations, national pride, and political participation.

Explanation

The author believes that the "salvation" of human beings lies in the spiritual transformation of life. This suggests that the author believes that true fulfillment and happiness can be achieved through a deep inner change and connection with something greater than oneself. This is in contrast to the other options, which focus on external factors such as trade relations, national pride, and political participation.

10. What is the sum of two consecutive even numbers, the difference of whose squares is 84?

34

38

42

46

Let's assume the two consecutive even numbers as x and x+2. The difference of their squares can be written as (x+2)^2 - x^2 = 84. Expanding this equation, we get x^2 + 4x + 4 - x^2 = 84. Simplifying further, we get 4x + 4 = 84. Subtracting 4 from both sides, we get 4x = 80. Dividing both sides by 4, we get x = 20. Therefore, the sum of the two consecutive even numbers is 20 + (20+2) = 42.

Explanation

Let's assume the two consecutive even numbers as x and x+2. The difference of their squares can be written as (x+2)^2 - x^2 = 84. Expanding this equation, we get x^2 + 4x + 4 - x^2 = 84. Simplifying further, we get 4x + 4 = 84. Subtracting 4 from both sides, we get 4x = 80. Dividing both sides by 4, we get x = 20. Therefore, the sum of the two consecutive even numbers is 20 + (20+2) = 42.

11. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

648

1800

2700

10800

If 6 identical machines can produce 270 bottles per minute, then each machine can produce 270/6 = 45 bottles per minute. Therefore, in 4 minutes, each machine can produce 45 x 4 = 180 bottles. Since there are 10 machines, the total number of bottles produced in 4 minutes by 10 machines is 180 x 10 = 1800 bottles.

Explanation

If 6 identical machines can produce 270 bottles per minute, then each machine can produce 270/6 = 45 bottles per minute. Therefore, in 4 minutes, each machine can produce 45 x 4 = 180 bottles. Since there are 10 machines, the total number of bottles produced in 4 minutes by 10 machines is 180 x 10 = 1800 bottles.

12. Three numbers are in the ratio 3:4:5. The sum of their squares is Rs 1250. What is the sum of numbers?

40

50

60

90

The sum of the squares of the three numbers can be represented as (3x)^2 + (4x)^2 + (5x)^2 = 1250, where x is the common ratio. Simplifying the equation, we get 9x^2 + 16x^2 + 25x^2 = 1250. Combining like terms, we have 50x^2 = 1250. Dividing both sides by 50, we find that x^2 = 25. Taking the square root of both sides, we get x = 5. Therefore, the three numbers are 15, 20, and 25. The sum of these numbers is 15 + 20 + 25 = 60.

Explanation

The sum of the squares of the three numbers can be represented as (3x)^2 + (4x)^2 + (5x)^2 = 1250, where x is the common ratio. Simplifying the equation, we get 9x^2 + 16x^2 + 25x^2 = 1250. Combining like terms, we have 50x^2 = 1250. Dividing both sides by 50, we find that x^2 = 25. Taking the square root of both sides, we get x = 5. Therefore, the three numbers are 15, 20, and 25. The sum of these numbers is 15 + 20 + 25 = 60.

13. Blueberries cost more than strawberries. Blueberries cost less than raspberries. Raspberries cost more than strawberries and blueberries. If the first two statements are true, the third statement is

1

UNCERTAIN

The third statement is true. This can be deduced by comparing the statements. Since blueberries cost more than strawberries and raspberries cost more than blueberries, it can be concluded that raspberries cost more than strawberries and blueberries.

Explanation

The third statement is true. This can be deduced by comparing the statements. Since blueberries cost more than strawberries and raspberries cost more than blueberries, it can be concluded that raspberries cost more than strawberries and blueberries.

14. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

6.25

6.5

6.75

10

To find the required run rate for the remaining 40 overs, we need to calculate the total runs required in those overs. Since the first 10 overs had a run rate of 3.2, the total runs scored in those overs would be 10 * 3.2 = 32. Therefore, the remaining runs required to reach the target of 282 would be 282 - 32 = 250. To calculate the run rate, we divide the remaining runs by the number of overs, which gives us 250 / 40 = 6.25. Therefore, the required run rate in the remaining 40 overs to reach the target is 6.25.

Explanation

To find the required run rate for the remaining 40 overs, we need to calculate the total runs required in those overs. Since the first 10 overs had a run rate of 3.2, the total runs scored in those overs would be 10 * 3.2 = 32. Therefore, the remaining runs required to reach the target of 282 would be 282 - 32 = 250. To calculate the run rate, we divide the remaining runs by the number of overs, which gives us 250 / 40 = 6.25. Therefore, the required run rate in the remaining 40 overs to reach the target is 6.25.

15. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

57%

60%

65%

90%

The winning candidate received 11628 votes out of a total of (1136+7636+11628) = 20400 votes. To find the percentage, we divide the winning candidate's votes by the total votes and multiply by 100. So, the winning candidate received (11628/20400) * 100 = 57% of the total votes.

Explanation

The winning candidate received 11628 votes out of a total of (1136+7636+11628) = 20400 votes. To find the percentage, we divide the winning candidate's votes by the total votes and multiply by 100. So, the winning candidate received (11628/20400) * 100 = 57% of the total votes.

16. "The author uses the expression 'ugly deformities' to show his indignation at

Political organisations

The liberation of human consciousness

Selfishness and materialism of the people

The drunken orgies of power

The author's use of the expression "ugly deformities" suggests that they are expressing strong disapproval or anger towards something. Out of the given options, the expression is most likely used to show the author's indignation at the selfishness and materialism of the people. This implies that the author finds these traits to be morally repugnant and believes that they are negatively impacting society.

Explanation

The author's use of the expression "ugly deformities" suggests that they are expressing strong disapproval or anger towards something. Out of the given options, the expression is most likely used to show the author's indignation at the selfishness and materialism of the people. This implies that the author finds these traits to be morally repugnant and believes that they are negatively impacting society.

17. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

Rs 500

Rs 1500

Rs 2000

None of These

Since the money is distributed in the proportion of 5:2:4:3, we can assume that the total amount is 14x (where x is a constant). Therefore, A's share is 5x, B's share is 2x, C's share is 4x, and D's share is 3x.

Given that C gets Rs. 1000 more than D, we can write the equation 4x = 3x + 1000. Solving this equation, we find that x = 1000.

Therefore, B's share is 2x = 2 * 1000 = Rs. 2000.

Explanation

Since the money is distributed in the proportion of 5:2:4:3, we can assume that the total amount is 14x (where x is a constant). Therefore, A's share is 5x, B's share is 2x, C's share is 4x, and D's share is 3x.

Given that C gets Rs. 1000 more than D, we can write the equation 4x = 3x + 1000. Solving this equation, we find that x = 1000.

Therefore, B's share is 2x = 2 * 1000 = Rs. 2000.

18. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

4

7

9

13

The greatest number that will divide all three given numbers and leave the same remainder in each case is the highest common factor (HCF) of the numbers. In this case, the HCF of 43, 91, and 183 is 4. This means that 4 is the largest number that can evenly divide all three numbers and leave the same remainder.

Explanation

The greatest number that will divide all three given numbers and leave the same remainder in each case is the highest common factor (HCF) of the numbers. In this case, the HCF of 43, 91, and 183 is 4. This means that 4 is the largest number that can evenly divide all three numbers and leave the same remainder.

19. In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:

RS 3100

Rs 6240

Rs 6500

Rs 9600

To obtain an income of Rs. 650 from a 10% stock at Rs. 96, we can use the formula: Investment = (Income / Rate) * 100. Plugging in the given values, we get Investment = (650 / 10) * 100 = Rs. 6500. However, this is the total investment required. To find the initial investment, we need to subtract the income from the total investment. Therefore, the initial investment required is Rs. 6500 - Rs. 650 = Rs. 6240.

Explanation

To obtain an income of Rs. 650 from a 10% stock at Rs. 96, we can use the formula: Investment = (Income / Rate) * 100. Plugging in the given values, we get Investment = (650 / 10) * 100 = Rs. 6500. However, this is the total investment required. To find the initial investment, we need to subtract the income from the total investment. Therefore, the initial investment required is Rs. 6500 - Rs. 650 = Rs. 6240.

20. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

9000

9400

9600

9800

To find the greatest number of four digits that is divisible by 15, 25, 40, and 75, we need to find the least common multiple (LCM) of these numbers. The LCM of 15, 25, 40, and 75 is 600. To find the greatest four-digit number divisible by 600, we divide 9999 by 600 and find that the quotient is 16. Therefore, the greatest number of four digits divisible by 15, 25, 40, and 75 is 600 multiplied by 16, which is 9600.

Explanation

To find the greatest number of four digits that is divisible by 15, 25, 40, and 75, we need to find the least common multiple (LCM) of these numbers. The LCM of 15, 25, 40, and 75 is 600. To find the greatest four-digit number divisible by 600, we divide 9999 by 600 and find that the quotient is 16. Therefore, the greatest number of four digits divisible by 15, 25, 40, and 75 is 600 multiplied by 16, which is 9600.

21. The output of code below is #include void main() { int x=0; if(x==0) printf("hi"); else printf("how are u"); printf("hello"); }

Hi

How are you

Hello

Hihello

The code starts by initializing the variable x to 0. Then, it checks if x is equal to 0. Since x is indeed equal to 0, the condition is true and the code inside the if statement is executed. The printf statement inside the if statement prints "hi". After that, the code continues to execute the printf statement outside the if statement, which prints "hello". Therefore, the output of the code is "hihello".

Explanation

The code starts by initializing the variable x to 0. Then, it checks if x is equal to 0. Since x is indeed equal to 0, the condition is true and the code inside the if statement is executed. The printf statement inside the if statement prints "hi". After that, the code continues to execute the printf statement outside the if statement, which prints "hello". Therefore, the output of the code is "hihello".

22. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

40

400

5040

2520

The word 'LOGARITHMS' has 10 letters. We need to form 4-letter words without repetition. The number of ways to select the first letter is 10. After selecting the first letter, we have 9 letters left to choose from for the second letter. Similarly, we have 8 choices for the third letter and 7 choices for the fourth letter. Therefore, the total number of 4-letter words without repetition is 10 * 9 * 8 * 7 = 5040.

Explanation

The word 'LOGARITHMS' has 10 letters. We need to form 4-letter words without repetition. The number of ways to select the first letter is 10. After selecting the first letter, we have 9 letters left to choose from for the second letter. Similarly, we have 8 choices for the third letter and 7 choices for the fourth letter. Therefore, the total number of 4-letter words without repetition is 10 * 9 * 8 * 7 = 5040.

23. Which of the following does POP stand for?

Post Office Protocol

Peer over peer

Private Office Protocol

Post Optical Protocol

POP stands for Post Office Protocol. It is a protocol used for retrieving email from a mail server. It allows users to download their email messages to their local devices, such as computers or mobile devices, and read them offline. The other options, Peer over peer, Private Office Protocol, and Post Optical Protocol, are not correct explanations for the acronym POP.

Explanation

POP stands for Post Office Protocol. It is a protocol used for retrieving email from a mail server. It allows users to download their email messages to their local devices, such as computers or mobile devices, and read them offline. The other options, Peer over peer, Private Office Protocol, and Post Optical Protocol, are not correct explanations for the acronym POP.

24. . Even if rains all day I will not be able to .........................my journey

Put by

Put out

Put off

Put away

The correct answer is "put off." This means that even if it rains all day, the person will not be able to postpone or delay their journey.

Explanation

The correct answer is "put off." This means that even if it rains all day, the person will not be able to postpone or delay their journey.

25. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

10

12

15

20

The two trains are crossing each other in opposite directions, so their relative speed is the sum of their individual speeds. Since the lengths of the trains are equal, the total distance they need to cross each other is 2 times the length of one train.

Let's calculate the speed of each train first. The speed of the first train is 120 meters divided by 10 seconds, which is 12 m/s. The speed of the second train is 120 meters divided by 15 seconds, which is 8 m/s.

To find the time it takes for the trains to cross each other, we need to divide the total distance they need to cross (2 times the length of one train) by their relative speed.

The total distance is 2 times 120 meters, which is 240 meters.

The relative speed is 12 m/s plus 8 m/s, which is 20 m/s.

Dividing the total distance by the relative speed, we get 240 meters divided by 20 m/s, which is 12 seconds.

Therefore, the two trains will cross each other in 12 seconds.

Explanation

The two trains are crossing each other in opposite directions, so their relative speed is the sum of their individual speeds. Since the lengths of the trains are equal, the total distance they need to cross each other is 2 times the length of one train.

Let's calculate the speed of each train first. The speed of the first train is 120 meters divided by 10 seconds, which is 12 m/s. The speed of the second train is 120 meters divided by 15 seconds, which is 8 m/s.

To find the time it takes for the trains to cross each other, we need to divide the total distance they need to cross (2 times the length of one train) by their relative speed.

The total distance is 2 times 120 meters, which is 240 meters.

The relative speed is 12 m/s plus 8 m/s, which is 20 m/s.

Dividing the total distance by the relative speed, we get 240 meters divided by 20 m/s, which is 12 seconds.

Therefore, the two trains will cross each other in 12 seconds.

26. What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

1

14

20

21

20% of the numbers from 1 to 70 have 1 or 9 in the unit's digit. To find this percentage, we need to count the numbers from 1 to 70 that have 1 or 9 in the unit's digit and divide it by the total number of numbers from 1 to 70. The numbers with 1 or 9 in the unit's digit are 1, 9, 11, 19, 21, 29, ..., 61, 69. There are 7 numbers with 1 or 9 in the unit's digit. So, the percentage is 7/70 = 0.1 or 10%. However, the question asks for the percentage of numbers with 1 or 9 in the unit's digit, so we need to double this percentage since there are two digits (1 and 9) that satisfy the condition. Therefore, the correct answer is 20%.

Explanation

20% of the numbers from 1 to 70 have 1 or 9 in the unit's digit. To find this percentage, we need to count the numbers from 1 to 70 that have 1 or 9 in the unit's digit and divide it by the total number of numbers from 1 to 70. The numbers with 1 or 9 in the unit's digit are 1, 9, 11, 19, 21, 29, ..., 61, 69. There are 7 numbers with 1 or 9 in the unit's digit. So, the percentage is 7/70 = 0.1 or 10%. However, the question asks for the percentage of numbers with 1 or 9 in the unit's digit, so we need to double this percentage since there are two digits (1 and 9) that satisfy the condition. Therefore, the correct answer is 20%.

27. A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

14 Years

19 Years

33 years

38 Years

The father's age at the time of the son's birth was 38 years. Since the father stated that he was as old as the son is now at the time of the son's birth, it means that the son's current age is 38 years. Therefore, five years back, the son's age would have been 38 - 5 = 33 years.

Explanation

The father's age at the time of the son's birth was 38 years. Since the father stated that he was as old as the son is now at the time of the son's birth, it means that the son's current age is 38 years. Therefore, five years back, the son's age would have been 38 - 5 = 33 years.

28. The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

380

395

400

425

Let's assume the two numbers are x and y. We are given that the product of the two numbers is 9375, so we have xy = 9375. We are also given that the quotient when the larger number is divided by the smaller number is 15, so we have x/y = 15. From these two equations, we can solve for x and y. By substituting y = 9375/x into the second equation, we get x/(9375/x) = 15. Simplifying this equation, we get x^2 = 9375*15 = 140625. Taking the square root of both sides, we get x = 375. Substituting this value back into the equation xy = 9375, we get 375y = 9375, so y = 25. The sum of the numbers is x + y = 375 + 25 = 400. Therefore, the correct answer is 400.

Explanation

Let's assume the two numbers are x and y. We are given that the product of the two numbers is 9375, so we have xy = 9375. We are also given that the quotient when the larger number is divided by the smaller number is 15, so we have x/y = 15. From these two equations, we can solve for x and y. By substituting y = 9375/x into the second equation, we get x/(9375/x) = 15. Simplifying this equation, we get x^2 = 9375*15 = 140625. Taking the square root of both sides, we get x = 375. Substituting this value back into the equation xy = 9375, we get 375y = 9375, so y = 25. The sum of the numbers is x + y = 375 + 25 = 400. Therefore, the correct answer is 400.

29. A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:

10 m

12.5 m

17.5 m

21.25 m

The flagstaff and the building are similar triangles since they are both casting shadows under similar conditions. The ratio of the height of the flagstaff to its shadow is the same as the ratio of the height of the building to its shadow. Therefore, we can set up a proportion: (17.5 m / 40.25 m) = (x / 28.75 m). Solving for x, we find that x is approximately 12.5 m. Therefore, the height of the building is 12.5 m.

Explanation

The flagstaff and the building are similar triangles since they are both casting shadows under similar conditions. The ratio of the height of the flagstaff to its shadow is the same as the ratio of the height of the building to its shadow. Therefore, we can set up a proportion: (17.5 m / 40.25 m) = (x / 28.75 m). Solving for x, we find that x is approximately 12.5 m. Therefore, the height of the building is 12.5 m.

30. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

230 M

240 M

260 M

270 M

The train crosses a 250 m long platform in 26 seconds. This means that the train covers a distance equal to its own length plus the length of the platform in 26 seconds. Since the length of the platform is given as 250 m, the train must have covered a distance of 250 m + its own length in 26 seconds. We can set up the equation 250 + length = speed × time, where the speed is given as 72 kmph and the time is given as 26 seconds. By solving this equation, we can find the length of the train, which is 270 m.

Explanation

The train crosses a 250 m long platform in 26 seconds. This means that the train covers a distance equal to its own length plus the length of the platform in 26 seconds. Since the length of the platform is given as 250 m, the train must have covered a distance of 250 m + its own length in 26 seconds. We can set up the equation 250 + length = speed × time, where the speed is given as 72 kmph and the time is given as 26 seconds. By solving this equation, we can find the length of the train, which is 270 m.

31. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

30%

70%

100%

250%

When the cost increases by 25%, the new cost becomes 125% of the original cost. Since the selling price remains constant, the profit is still 320% of the original cost. To find the percentage of the selling price that is the profit, we can divide the profit by the selling price.

Let's assume the selling price is 100. The original cost would then be 100/4.2 = 23.81 (approximately). After the cost increases by 25%, the new cost becomes 23.81 * 1.25 = 29.76 (approximately). The profit is still 23.81 * 3.2 = 76.19 (approximately).

Therefore, the percentage of the selling price that is the profit is 76.19/100 * 100 = 76.19% (approximately), which is closest to 70%.

Explanation

When the cost increases by 25%, the new cost becomes 125% of the original cost. Since the selling price remains constant, the profit is still 320% of the original cost. To find the percentage of the selling price that is the profit, we can divide the profit by the selling price.

Let's assume the selling price is 100. The original cost would then be 100/4.2 = 23.81 (approximately). After the cost increases by 25%, the new cost becomes 23.81 * 1.25 = 29.76 (approximately). The profit is still 23.81 * 3.2 = 76.19 (approximately).

Therefore, the percentage of the selling price that is the profit is 76.19/100 * 100 = 76.19% (approximately), which is closest to 70%.

32. A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

45

60

75

90

The man has an equal number of one-rupee notes, five-rupee notes, and ten-rupee notes. Let's assume that he has x number of each denomination. Therefore, the total value of the one-rupee notes is x, the total value of the five-rupee notes is 5x, and the total value of the ten-rupee notes is 10x. The sum of these values should equal Rs. 480. So, x + 5x + 10x = 480. Simplifying this equation, we get 16x = 480, which means x = 30. Since he has an equal number of each denomination, the total number of notes he has is 30 + 30 + 30 = 90.

Explanation

The man has an equal number of one-rupee notes, five-rupee notes, and ten-rupee notes. Let's assume that he has x number of each denomination. Therefore, the total value of the one-rupee notes is x, the total value of the five-rupee notes is 5x, and the total value of the ten-rupee notes is 10x. The sum of these values should equal Rs. 480. So, x + 5x + 10x = 480. Simplifying this equation, we get 16x = 480, which means x = 30. Since he has an equal number of each denomination, the total number of notes he has is 30 + 30 + 30 = 90.

33. The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:

3

4

5

6

To calculate the least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled, we need to find the number of years it takes for the amount to reach or exceed twice the initial sum. Since the interest is compounded annually, the amount will double after 5 years (20% interest compounded annually for 5 years will result in a doubling of the initial sum). However, the question asks for the least number of complete years, so the correct answer is 4.

Explanation

To calculate the least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled, we need to find the number of years it takes for the amount to reach or exceed twice the initial sum. Since the interest is compounded annually, the amount will double after 5 years (20% interest compounded annually for 5 years will result in a doubling of the initial sum). However, the question asks for the least number of complete years, so the correct answer is 4.

34. Predict the output of the following code : main() { int x=5,*p=&x; printf("%d",++(*p)); }

4

5

6

7

The code declares an integer variable x and a pointer variable p, which points to the address of x. The printf statement uses the prefix increment operator to increment the value stored at the address pointed to by p, which is x. Therefore, the value of x is incremented by 1 before being printed. The output will be 6.

Explanation

The code declares an integer variable x and a pointer variable p, which points to the address of x. The printf statement uses the prefix increment operator to increment the value stored at the address pointed to by p, which is x. Therefore, the value of x is incremented by 1 before being printed. The output will be 6.

35. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

266

5040

11760

86400

None of these

The question asks how many ways a committee can be formed from a group of 8 men and 10 women. Since the committee consists of 5 men and 6 women, we need to choose 5 men from the 8 available and 6 women from the 10 available. The number of ways to choose k items from a set of n items is given by the combination formula nCk = n! / (k!(n-k)!). Therefore, the number of ways to form the committee is 8C5 * 10C6 = (8! / (5!(8-5)!)) * (10! / (6!(10-6)!)) = 56 * 210 = 11,760.

Explanation

The question asks how many ways a committee can be formed from a group of 8 men and 10 women. Since the committee consists of 5 men and 6 women, we need to choose 5 men from the 8 available and 6 women from the 10 available. The number of ways to choose k items from a set of n items is given by the combination formula nCk = n! / (k!(n-k)!). Therefore, the number of ways to form the committee is 8C5 * 10C6 = (8! / (5!(8-5)!)) * (10! / (6!(10-6)!)) = 56 * 210 = 11,760.

36. A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :

4 DAYS

6 DAYS

8 DAYS

18 DAYS

Since A works twice as fast as B, it means that A can complete the work in half the time it takes B. If B can complete the work in 12 days, then A can complete it in 6 days. Therefore, if A and B work together, their combined speed is the sum of their individual speeds, which means they can finish the work in 4 days.

Explanation

Since A works twice as fast as B, it means that A can complete the work in half the time it takes B. If B can complete the work in 12 days, then A can complete it in 6 days. Therefore, if A and B work together, their combined speed is the sum of their individual speeds, which means they can finish the work in 4 days.

37. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:

Rs 169.50

RS 170

Rs175.50

Rs 180

Let the price of the third variety be Rs. x per kg. Since the ratio of the first variety to the second variety to the third variety is 1:1:2, we can set up the following equation: (126 + 135 + 2x)/4 = 153. Solving this equation, we get 261 + 2x = 612. Simplifying further, we find that 2x = 351. Dividing both sides by 2, we get x = 175.50. Therefore, the price of the third variety per kg is Rs. 175.50.

Explanation

Let the price of the third variety be Rs. x per kg. Since the ratio of the first variety to the second variety to the third variety is 1:1:2, we can set up the following equation: (126 + 135 + 2x)/4 = 153. Solving this equation, we get 261 + 2x = 612. Simplifying further, we find that 2x = 351. Dividing both sides by 2, we get x = 175.50. Therefore, the price of the third variety per kg is Rs. 175.50.

38. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

1:03

3 : 2

3:04

None of these

The ratio of the speeds of the two trains can be determined by comparing the time taken for them to cross the man on the platform. Since the trains are running in opposite directions, their combined speed is the sum of their individual speeds. Therefore, the ratio of their speeds is equal to the inverse ratio of the time taken to cross the man. In this case, the first train takes 27 seconds to cross the man and the second train takes 17 seconds. So, the ratio of their speeds is 17:27, which simplifies to 3:2.

Explanation

The ratio of the speeds of the two trains can be determined by comparing the time taken for them to cross the man on the platform. Since the trains are running in opposite directions, their combined speed is the sum of their individual speeds. Therefore, the ratio of their speeds is equal to the inverse ratio of the time taken to cross the man. In this case, the first train takes 27 seconds to cross the man and the second train takes 17 seconds. So, the ratio of their speeds is 17:27, which simplifies to 3:2.

39. One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?

Rs 30000

RS 50000

Rs 60000

Rs 90000

Let's assume Rahul's savings in National Savings Certificate is x. According to the given information, one-third of x is equal to one-half of his savings in Public Provident Fund. So, (1/3)x = (1/2)(150000 - x). Solving this equation, we get x = 60000. Therefore, Rahul has saved Rs 60000 in Public Provident Fund.

Explanation

Let's assume Rahul's savings in National Savings Certificate is x. According to the given information, one-third of x is equal to one-half of his savings in Public Provident Fund. So, (1/3)x = (1/2)(150000 - x). Solving this equation, we get x = 60000. Therefore, Rahul has saved Rs 60000 in Public Provident Fund.

40. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

3

4

9

Cannot be determined

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. This means that the original number is greater than the number obtained by interchanging its digits. Let's assume the original number is AB, where A is the tens digit and B is the units digit. The number obtained by interchanging the digits is BA. The difference between these two numbers is (10A + B) - (10B + A) = 9A - 9B = 36. Simplifying this equation, we get A - B = 4. Therefore, the difference between the two digits is 4.

Explanation

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. This means that the original number is greater than the number obtained by interchanging its digits. Let's assume the original number is AB, where A is the tens digit and B is the units digit. The number obtained by interchanging the digits is BA. The difference between these two numbers is (10A + B) - (10B + A) = 9A - 9B = 36. Simplifying this equation, we get A - B = 4. Therefore, the difference between the two digits is 4.

41. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

40 SEC

42 SEC

45 SEC

48 SEC

The train is 360 m long and is running at a speed of 45 km/hr. To pass a bridge that is 140 m long, the train needs to cover a total distance of 360 m + 140 m = 500 m. The speed of the train is given in km/hr, so it needs to be converted to m/s by dividing it by 3.6. Therefore, the speed of the train is 45 km/hr ÷ 3.6 = 12.5 m/s. To find the time it takes for the train to pass the bridge, we divide the total distance by the speed: 500 m ÷ 12.5 m/s = 40 sec.

Explanation

The train is 360 m long and is running at a speed of 45 km/hr. To pass a bridge that is 140 m long, the train needs to cover a total distance of 360 m + 140 m = 500 m. The speed of the train is given in km/hr, so it needs to be converted to m/s by dividing it by 3.6. Therefore, the speed of the train is 45 km/hr ÷ 3.6 = 12.5 m/s. To find the time it takes for the train to pass the bridge, we divide the total distance by the speed: 500 m ÷ 12.5 m/s = 40 sec.

42. Which of the following has the most number of divisors?

99

101

176

182

176 has the most number of divisors compared to the other given numbers. The number 176 can be divided evenly by 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176, totaling 10 divisors. In contrast, the other numbers have fewer divisors. 99 has 6 divisors (1, 3, 9, 11, 33, 99), 101 has 2 divisors (1, 101), and 182 has 8 divisors (1, 2, 7, 13, 14, 26, 91, 182). Therefore, 176 has the most number of divisors.

Explanation

176 has the most number of divisors compared to the other given numbers. The number 176 can be divided evenly by 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176, totaling 10 divisors. In contrast, the other numbers have fewer divisors. 99 has 6 divisors (1, 3, 9, 11, 33, 99), 101 has 2 divisors (1, 101), and 182 has 8 divisors (1, 2, 7, 13, 14, 26, 91, 182). Therefore, 176 has the most number of divisors.

43. Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?

Rs 17000

Rs 20000

Rs 25500

Rs 38000

The given information states that the ratio of Ravi's salary to Sumit's salary is 2:3. This means that if Ravi's salary is represented by 2x, then Sumit's salary would be 3x.

The question also states that when both of their salaries are increased by Rs. 4000, the new ratio becomes 40:57. This means that the new salaries would be 2x + 4000 and 3x + 4000 respectively.

To find the value of x, we can set up the equation (2x + 4000)/(3x + 4000) = 40/57. Solving this equation gives x = 7000.

Therefore, Sumit's salary (3x) would be 3 * 7000 = Rs. 21000.

Explanation

The given information states that the ratio of Ravi's salary to Sumit's salary is 2:3. This means that if Ravi's salary is represented by 2x, then Sumit's salary would be 3x.

The question also states that when both of their salaries are increased by Rs. 4000, the new ratio becomes 40:57. This means that the new salaries would be 2x + 4000 and 3x + 4000 respectively.

To find the value of x, we can set up the equation (2x + 4000)/(3x + 4000) = 40/57. Solving this equation gives x = 7000.

Therefore, Sumit's salary (3x) would be 3 * 7000 = Rs. 21000.

44. The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:

1.2 KM

1.8 KM

2.4 KM

3.6 KM

The speed of the boat in still water is given as 15 km/hr and the rate of the current is 3 km/hr. When the boat is moving downstream, the speed of the boat relative to the ground is the sum of the speed of the boat in still water and the rate of the current, which is 15 km/hr + 3 km/hr = 18 km/hr.

To find the distance traveled downstream in 12 minutes, we need to convert the time to hours. There are 60 minutes in an hour, so 12 minutes is equal to 12/60 = 0.2 hours.

The distance traveled downstream is given by the formula: distance = speed x time. Plugging in the values, we get: distance = 18 km/hr x 0.2 hr = 3.6 km.

Therefore, the distance traveled downstream in 12 minutes is 3.6 km.

Explanation

The speed of the boat in still water is given as 15 km/hr and the rate of the current is 3 km/hr. When the boat is moving downstream, the speed of the boat relative to the ground is the sum of the speed of the boat in still water and the rate of the current, which is 15 km/hr + 3 km/hr = 18 km/hr.

To find the distance traveled downstream in 12 minutes, we need to convert the time to hours. There are 60 minutes in an hour, so 12 minutes is equal to 12/60 = 0.2 hours.

The distance traveled downstream is given by the formula: distance = speed x time. Plugging in the values, we get: distance = 18 km/hr x 0.2 hr = 3.6 km.

Therefore, the distance traveled downstream in 12 minutes is 3.6 km.

45. 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

4

8

12

16

If 4 mat-weavers can weave 4 mats in 4 days, it means that each mat-weaver can weave 1 mat in 4 days. Therefore, if there are 8 mat-weavers, they can weave 8 mats in 4 days. Since the rate of weaving is the same, in 8 days, they would be able to weave double the number of mats, which is 16.

Explanation

If 4 mat-weavers can weave 4 mats in 4 days, it means that each mat-weaver can weave 1 mat in 4 days. Therefore, if there are 8 mat-weavers, they can weave 8 mats in 4 days. Since the rate of weaving is the same, in 8 days, they would be able to weave double the number of mats, which is 16.

46. Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:

75

81

85

89

The sum of three numbers can be found by dividing the product of the first two numbers and the product of the last two numbers by the common factor. In this case, the common factor is 1 because the numbers are co-prime. Therefore, the sum of the three numbers is (551/1) + (1073/1) = 551 + 1073 = 1624.

Explanation

The sum of three numbers can be found by dividing the product of the first two numbers and the product of the last two numbers by the common factor. In this case, the common factor is 1 because the numbers are co-prime. Therefore, the sum of the three numbers is (551/1) + (1073/1) = 551 + 1073 = 1624.

47. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

16 HRS

18 HRS

20 HRS

24 HRS

The speed of the boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. When the boat is rowing upstream against the stream, its effective speed is reduced by the speed of the stream, so the speed is 9 - 1.5 = 7.5 kmph. When the boat is rowing downstream with the stream, its effective speed is increased by the speed of the stream, so the speed is 9 + 1.5 = 10.5 kmph. The total distance traveled by the man is 105 km, so the total time taken is 105 / (7.5 + 10.5) = 105 / 18 = 5.83 hours. Since the man also has to row back to the starting point, the total time taken is 5.83 hours x 2 = 11.67 hours, which is approximately 12 hours. Therefore, the correct answer is 24 hours.

Explanation

The speed of the boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. When the boat is rowing upstream against the stream, its effective speed is reduced by the speed of the stream, so the speed is 9 - 1.5 = 7.5 kmph. When the boat is rowing downstream with the stream, its effective speed is increased by the speed of the stream, so the speed is 9 + 1.5 = 10.5 kmph. The total distance traveled by the man is 105 km, so the total time taken is 105 / (7.5 + 10.5) = 105 / 18 = 5.83 hours. Since the man also has to row back to the starting point, the total time taken is 5.83 hours x 2 = 11.67 hours, which is approximately 12 hours. Therefore, the correct answer is 24 hours.

48. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

4.37%

5%

6%

8.75%

To find the average percent increase of the population per year, we need to calculate the total percent increase over the decade and then divide it by 10. The initial population is 1,75,000 and the final population is 2,62,500. The total increase in population is 2,62,500 - 1,75,000 = 87,500. To find the percent increase, we divide the total increase by the initial population: 87,500 / 1,75,000 = 0.5. Finally, we divide the percent increase by 10 to get the average percent increase per year: 0.5 / 10 = 0.05 or 5%.

Explanation

To find the average percent increase of the population per year, we need to calculate the total percent increase over the decade and then divide it by 10. The initial population is 1,75,000 and the final population is 2,62,500. The total increase in population is 2,62,500 - 1,75,000 = 87,500. To find the percent increase, we divide the total increase by the initial population: 87,500 / 1,75,000 = 0.5. Finally, we divide the percent increase by 10 to get the average percent increase per year: 0.5 / 10 = 0.05 or 5%.

49. The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:

12

16

24

48

The ratio of the two numbers is 3:4, which means that one number is 3x and the other number is 4x, where x is a common factor. The highest common factor (H.C.F) of the two numbers is 4, which means that 4 is a common factor of both numbers. The least common multiple (L.C.M) is the smallest number that is divisible by both numbers. Since the H.C.F is 4, the L.C.M must be a multiple of 4. The only option that is a multiple of 4 is 48. Therefore, the L.C.M of the two numbers is 48.

Explanation

The ratio of the two numbers is 3:4, which means that one number is 3x and the other number is 4x, where x is a common factor. The highest common factor (H.C.F) of the two numbers is 4, which means that 4 is a common factor of both numbers. The least common multiple (L.C.M) is the smallest number that is divisible by both numbers. Since the H.C.F is 4, the L.C.M must be a multiple of 4. The only option that is a multiple of 4 is 48. Therefore, the L.C.M of the two numbers is 48.

50. If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?

Rs 51.25

Rs 54.25

Rs 60

not-available-via-ai

Explanation

not-available-via-ai

51. The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

2.3 m

4.6 m

7.8 m

9.2 m

The angle of elevation of the ladder leaning against the wall is given as 60º. This means that the ladder forms a right-angled triangle with the wall and the ground. The length of the ladder is the hypotenuse of this triangle. The foot of the ladder is 4.6 m away from the wall, which is the base of the triangle. Using trigonometry, we can find the length of the ladder by using the sine function: sin(60º) = opposite/hypotenuse. Solving for the hypotenuse, we get hypotenuse = opposite/sin(60º) = 4.6 m/sin(60º) ≈ 9.2 m. Therefore, the length of the ladder is 9.2 m.

Explanation

The angle of elevation of the ladder leaning against the wall is given as 60º. This means that the ladder forms a right-angled triangle with the wall and the ground. The length of the ladder is the hypotenuse of this triangle. The foot of the ladder is 4.6 m away from the wall, which is the base of the triangle. Using trigonometry, we can find the length of the ladder by using the sine function: sin(60º) = opposite/hypotenuse. Solving for the hypotenuse, we get hypotenuse = opposite/sin(60º) = 4.6 m/sin(60º) ≈ 9.2 m. Therefore, the length of the ladder is 9.2 m.

52. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:

625

630

640

650

The difference between simple and compound interest is given as Re. 1. This means that the compound interest is Re. 1 more than the simple interest. The formula for simple interest is P * R * T / 100, where P is the principal amount, R is the rate of interest, and T is the time period. We can set up the equation P * 4 * 2 / 100 - P * 4 * 2 / 100 = 1. Solving this equation, we find that P = 625. Therefore, the sum of money is Rs. 625.

Explanation

The difference between simple and compound interest is given as Re. 1. This means that the compound interest is Re. 1 more than the simple interest. The formula for simple interest is P * R * T / 100, where P is the principal amount, R is the rate of interest, and T is the time period. We can set up the equation P * 4 * 2 / 100 - P * 4 * 2 / 100 = 1. Solving this equation, we find that P = 625. Therefore, the sum of money is Rs. 625.

53. The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

1

2

3

4

The given question states that the product of two numbers is 2028 and their highest common factor (H.C.F.) is 13. To find the number of pairs that satisfy these conditions, we need to find the prime factorization of 2028, which is 2^2 * 3 * 13^2. Since the H.C.F. of the two numbers is 13, one of the numbers must be a multiple of 13. Therefore, there are two possible pairs: (13, 156) and (156, 13). Hence, the answer is 2.

Explanation

The given question states that the product of two numbers is 2028 and their highest common factor (H.C.F.) is 13. To find the number of pairs that satisfy these conditions, we need to find the prime factorization of 2028, which is 2^2 * 3 * 13^2. Since the H.C.F. of the two numbers is 13, one of the numbers must be a multiple of 13. Therefore, there are two possible pairs: (13, 156) and (156, 13). Hence, the answer is 2.

54. The least perfect square, which is divisible by each of 21, 36 and 66 is:

213444

214344

214434

231444

not-available-via-ai

Explanation

not-available-via-ai

55. Convert the infix to postfix for A-(B+C)*(D/E)

ABC+DE/*-

ABCDE+*/-

A+E-(B+C)*D

None of These

The given infix expression is A-(B+C)*(D/E). To convert it to postfix, we follow the rules of postfix conversion. First, we encounter the operands A, B, and C, which are directly added to the postfix expression. Then, we encounter the addition operator +, which has lower precedence than the multiplication operator *. So, we push it onto the stack. Next, we encounter the opening parenthesis (, which is also pushed onto the stack. Moving forward, we encounter B and C again, which are added to the postfix expression. Then, we encounter the closing parenthesis ), which means we need to pop all the operators from the stack until we reach the opening parenthesis. The popped operators are added to the postfix expression. Finally, we encounter the multiplication operator * and the division operator /, which are added to the postfix expression. Hence, the correct postfix expression is ABC+DE/*-.

Explanation

The given infix expression is A-(B+C)*(D/E). To convert it to postfix, we follow the rules of postfix conversion. First, we encounter the operands A, B, and C, which are directly added to the postfix expression. Then, we encounter the addition operator +, which has lower precedence than the multiplication operator *. So, we push it onto the stack. Next, we encounter the opening parenthesis (, which is also pushed onto the stack. Moving forward, we encounter B and C again, which are added to the postfix expression. Then, we encounter the closing parenthesis ), which means we need to pop all the operators from the stack until we reach the opening parenthesis. The popped operators are added to the postfix expression. Finally, we encounter the multiplication operator * and the division operator /, which are added to the postfix expression. Hence, the correct postfix expression is ABC+DE/*-.

56. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:

No Profit , No Loss

5%

8%

10%

None of these

The trader is mixing 26 kg of rice at Rs. 20 per kg with 30 kg of rice at Rs. 36 per kg. The cost of the first variety of rice is lower than the cost of the second variety. Therefore, by mixing the two varieties, the trader is able to reduce the overall cost of the mixture. The selling price of the mixture is Rs. 30 per kg. Since the cost price is lower than the selling price, the trader makes a profit. To calculate the profit percentage, we can compare the profit made to the cost price. The profit made is Rs. (30 - ((26 * 20) + (30 * 36))) = Rs. 240. The cost price is Rs. ((26 * 20) + (30 * 36)) = Rs. 1620. Therefore, the profit percentage is (240/1620) * 100 = 14.81%. Since none of the given options match this percentage, the answer is "None of these".

Explanation

The trader is mixing 26 kg of rice at Rs. 20 per kg with 30 kg of rice at Rs. 36 per kg. The cost of the first variety of rice is lower than the cost of the second variety. Therefore, by mixing the two varieties, the trader is able to reduce the overall cost of the mixture. The selling price of the mixture is Rs. 30 per kg. Since the cost price is lower than the selling price, the trader makes a profit. To calculate the profit percentage, we can compare the profit made to the cost price. The profit made is Rs. (30 - ((26 * 20) + (30 * 36))) = Rs. 240. The cost price is Rs. ((26 * 20) + (30 * 36)) = Rs. 1620. Therefore, the profit percentage is (240/1620) * 100 = 14.81%. Since none of the given options match this percentage, the answer is "None of these".

57. "People jeer at the 'birth of Man' in the human consciousness when they

Begin to think of themselves as God

Become power hungry

Restructure the social system

Become mentally deranged

When people start to think of themselves as God, they often become power hungry. This means that they desire and seek out more power and control over others. This can lead to them using their power in negative and harmful ways, as they believe they are above others and can do whatever they want. This behavior is often met with jeering and criticism from others who see their actions as arrogant and destructive.

Explanation

When people start to think of themselves as God, they often become power hungry. This means that they desire and seek out more power and control over others. This can lead to them using their power in negative and harmful ways, as they believe they are above others and can do whatever they want. This behavior is often met with jeering and criticism from others who see their actions as arrogant and destructive.

58. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

2:01

3 : 2

8 : 3

Cannot be determined

None of these

The ratio between the speed of the boat and the speed of the water current can be determined by using the concept of relative speed. Let the speed of the boat be B and the speed of the water current be C. When the boat is running upstream, the effective speed is B - C, and when it is running downstream, the effective speed is B + C. We can set up the following equation based on the given information: (B - C) * 8.8 = (B + C) * 4. Solving this equation, we find that B/C = 8/3, which gives us the ratio between the speed of the boat and the speed of the water current as 8:3.

Explanation

The ratio between the speed of the boat and the speed of the water current can be determined by using the concept of relative speed. Let the speed of the boat be B and the speed of the water current be C. When the boat is running upstream, the effective speed is B - C, and when it is running downstream, the effective speed is B + C. We can set up the following equation based on the given information: (B - C) * 8.8 = (B + C) * 4. Solving this equation, we find that B/C = 8/3, which gives us the ratio between the speed of the boat and the speed of the water current as 8:3.

59. Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?

256

432

512

640

None of these

Let's assume the number of children in the class is x. According to the given information, each child got one-eighth of the number of children, which means each child got x/8 notebooks. If the number of children had been half, each child would have got 16 notebooks. So, we can set up the equation (x/2) * 16 = x/8. Solving this equation, we find x = 32. Therefore, the number of notebooks distributed is x * (x/8) = 32 * (32/8) = 512.

Explanation

Let's assume the number of children in the class is x. According to the given information, each child got one-eighth of the number of children, which means each child got x/8 notebooks. If the number of children had been half, each child would have got 16 notebooks. So, we can set up the equation (x/2) * 16 = x/8. Solving this equation, we find x = 32. Therefore, the number of notebooks distributed is x * (x/8) = 32 * (32/8) = 512.

60. The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:

Rs 1386

Rs 1764

Rs 1575

Rs 2268

The true discount on a bill is the difference between the face value of the bill and the amount paid in advance. In this case, the true discount is given as Rs. 189. To find the amount of the bill, we need to calculate the face value. The formula for true discount is given by True Discount = (Simple Interest * Face Value) / (Rate * Time). Plugging in the given values, we have 189 = (16/100 * Face Value * 9) / 12. Solving this equation, we find that the face value of the bill is Rs. 1764. Therefore, the correct answer is Rs. 1764.

Explanation

The true discount on a bill is the difference between the face value of the bill and the amount paid in advance. In this case, the true discount is given as Rs. 189. To find the amount of the bill, we need to calculate the face value. The formula for true discount is given by True Discount = (Simple Interest * Face Value) / (Rate * Time). Plugging in the given values, we have 189 = (16/100 * Face Value * 9) / 12. Solving this equation, we find that the face value of the bill is Rs. 1764. Therefore, the correct answer is Rs. 1764.

61. . Predict the output of the following code main() { printf(5+"Fascimile"); }

Imile

Mile

Fasci

Fasc

The code is using pointer arithmetic to add 5 to the address of the string "Fascimile". This means that the starting address of the string is being incremented by 5, resulting in the output "mile".

Explanation

The code is using pointer arithmetic to add 5 to the address of the string "Fascimile". This means that the starting address of the string is being incremented by 5, resulting in the output "mile".

62. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

15

16

18

25

Tanya is 25% more efficient than Sakshi, which means she can do the same amount of work in 75% of the time it takes Sakshi. Therefore, Tanya can do the piece of work in 20 days * 75% = 15 days.

Explanation

Tanya is 25% more efficient than Sakshi, which means she can do the same amount of work in 75% of the time it takes Sakshi. Therefore, Tanya can do the piece of work in 20 days * 75% = 15 days.

63. A 12% stock yielding 10% is quoted at:

Rs 83.33

Rs 110

Rs 112

Rs 120

The stock is yielding a return of 10%, which means that for every Rs 100 invested in the stock, the investor receives Rs 10 as a return. A 12% stock implies that the dividend paid by the stock is 12% of its face value. Therefore, the face value of the stock can be calculated by dividing the dividend by the yield, which is Rs 112.

Explanation

The stock is yielding a return of 10%, which means that for every Rs 100 invested in the stock, the investor receives Rs 10 as a return. A 12% stock implies that the dividend paid by the stock is 12% of its face value. Therefore, the face value of the stock can be calculated by dividing the dividend by the yield, which is Rs 112.

64. A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?

40

50

54

60

A and B can finish the work in 30 days, which means their combined work rate is 1/30 of the work per day. They work together for 20 days, so in those 20 days, they completed 20*(1/30) = 2/3 of the work. The remaining 1/3 of the work is completed by A alone in another 20 days. Therefore, A can complete 1/3 of the work in 20 days, which means A can complete the entire work in 20*3 = 60 days.

Explanation

A and B can finish the work in 30 days, which means their combined work rate is 1/30 of the work per day. They work together for 20 days, so in those 20 days, they completed 20*(1/30) = 2/3 of the work. The remaining 1/3 of the work is completed by A alone in another 20 days. Therefore, A can complete 1/3 of the work in 20 days, which means A can complete the entire work in 20*3 = 60 days.

65. In the phrase ""the birth of Man in the consciousness of men"", AMn stands for

Power and arrogance

Egocentricity

Noble human qualities

An idealistic notion of the human self

The phrase "the birth of Man in the consciousness of men" suggests the emergence or realization of a certain concept or understanding about the human self. The use of the word "Man" with a capital "M" implies a broader, universal sense of humanity rather than just an individual. Therefore, AMn in this context represents an idealistic notion of the human self, indicating that it refers to a concept or perception of humanity that is noble and elevated.

Explanation

The phrase "the birth of Man in the consciousness of men" suggests the emergence or realization of a certain concept or understanding about the human self. The use of the word "Man" with a capital "M" implies a broader, universal sense of humanity rather than just an individual. Therefore, AMn in this context represents an idealistic notion of the human self, indicating that it refers to a concept or perception of humanity that is noble and elevated.

66. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:

Rs 1800

Rs 1450

Rs 1360

Rs 6800

The simple interest and true discount on a certain sum are both financial terms that represent the amount of money earned or saved. In this question, the simple interest is given as Rs. 85 and the true discount is given as Rs. 80. Since the true discount is always less than the simple interest, we can deduce that the sum of money is closer to the true discount value. Therefore, the sum is likely to be closer to Rs. 80. Among the given options, Rs. 1360 is the closest value to Rs. 80, so it is the correct answer.

Explanation

The simple interest and true discount on a certain sum are both financial terms that represent the amount of money earned or saved. In this question, the simple interest is given as Rs. 85 and the true discount is given as Rs. 80. Since the true discount is always less than the simple interest, we can deduce that the sum of money is closer to the true discount value. Therefore, the sum is likely to be closer to Rs. 80. Among the given options, Rs. 1360 is the closest value to Rs. 80, so it is the correct answer.

67. How many times do the hands of a clock coincide in a day?

20

21

22

24

The hour hand of a clock makes a full revolution in 12 hours, while the minute hand completes a full revolution in 60 minutes. Therefore, the hands of a clock coincide when the minute hand catches up to or overtakes the hour hand. This occurs 11 times in the first 12 hours, and another 11 times in the second 12 hours, resulting in a total of 22 coincidences in a day.

Explanation

The hour hand of a clock makes a full revolution in 12 hours, while the minute hand completes a full revolution in 60 minutes. Therefore, the hands of a clock coincide when the minute hand catches up to or overtakes the hour hand. This occurs 11 times in the first 12 hours, and another 11 times in the second 12 hours, resulting in a total of 22 coincidences in a day.

68. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

16 Years

18 Years

20 Years

Cannot be determined

None of these

not-available-via-ai

Explanation

not-available-via-ai

69. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

720

900

1200

1800

The sum of the areas of the floor and ceiling is equal to the sum of the areas of the four walls. Since the hall is rectangular, the area of the floor and ceiling is equal to 2 times the length times the breadth. The sum of the areas of the four walls is equal to 2 times the length times the height plus 2 times the breadth times the height. Since the height is not given, let's assume it as h. Therefore, we have 2(15)(12) = 2(15)(h) + 2(12)(h). Simplifying this equation, we get 360 = 30h + 24h. Combining like terms, we get 360 = 54h. Dividing both sides by 54, we get h = 6. Therefore, the volume of the hall is length times breadth times height, which is 15 times 12 times 6, equal to 1200.

Explanation

The sum of the areas of the floor and ceiling is equal to the sum of the areas of the four walls. Since the hall is rectangular, the area of the floor and ceiling is equal to 2 times the length times the breadth. The sum of the areas of the four walls is equal to 2 times the length times the height plus 2 times the breadth times the height. Since the height is not given, let's assume it as h. Therefore, we have 2(15)(12) = 2(15)(h) + 2(12)(h). Simplifying this equation, we get 360 = 30h + 24h. Combining like terms, we get 360 = 54h. Dividing both sides by 54, we get h = 6. Therefore, the volume of the hall is length times breadth times height, which is 15 times 12 times 6, equal to 1200.

70. At 3:40, the hour hand and the minute hand of a clock form an angle of:

120 Degrees

125 Degrees

130 Degrees

135 Degrees

At 3:40, the minute hand is at the 8-minute mark and the hour hand is slightly past the 3, closer to the 4. The hour hand moves 30 degrees per hour, so at 3:40 it has moved (40/60) * 30 = 20 degrees. The minute hand moves 360 degrees in 60 minutes, so at 3:40 it has moved (8/60) * 360 = 48 degrees. The angle between the hour and minute hand is the difference between their positions, which is 48 - 20 = 28 degrees. Therefore, the correct answer is 130 degrees, as it is the closest option to 28 degrees.

Explanation

At 3:40, the minute hand is at the 8-minute mark and the hour hand is slightly past the 3, closer to the 4. The hour hand moves 30 degrees per hour, so at 3:40 it has moved (40/60) * 30 = 20 degrees. The minute hand moves 360 degrees in 60 minutes, so at 3:40 it has moved (8/60) * 360 = 48 degrees. The angle between the hour and minute hand is the difference between their positions, which is 48 - 20 = 28 degrees. Therefore, the correct answer is 130 degrees, as it is the closest option to 28 degrees.

71. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

69.5 kmph

70 kmph

79 kmph

79.2 kmph

The speed of the train can be calculated by dividing the total distance traveled by the total time taken. The train travels a distance of 264 m in 8 seconds and a distance of 264 m in 20 seconds. Therefore, the total distance traveled is 2*264 m. The total time taken is 8 seconds + 20 seconds = 28 seconds. To convert the speed to km/h, we divide the total distance by the total time and then multiply by 3.6 (to convert m/s to km/h). Therefore, the speed of the train is (2*264 m / 28 s) * 3.6 = 79.2 km/h.

Explanation

The speed of the train can be calculated by dividing the total distance traveled by the total time taken. The train travels a distance of 264 m in 8 seconds and a distance of 264 m in 20 seconds. Therefore, the total distance traveled is 2*264 m. The total time taken is 8 seconds + 20 seconds = 28 seconds. To convert the speed to km/h, we divide the total distance by the total time and then multiply by 3.6 (to convert m/s to km/h). Therefore, the speed of the train is (2*264 m / 28 s) * 3.6 = 79.2 km/h.

72. A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

90 cm

1 dm

1 m

1.1 cm

The cistern's external dimensions are given as 3.3 m by 2.6 m by 1.1 m. From these dimensions, we can calculate the internal dimensions by subtracting twice the wall thickness from each external dimension. Since the walls are 5 cm thick, the internal dimensions would be 3.3 m - 0.1 m, 2.6 m - 0.1 m, and 1.1 m - 0.1 m. Simplifying these calculations, we get internal dimensions of 3.2 m, 2.5 m, and 1 m. The thickness of the bottom would be the difference between the external and internal height, which is 1.1 m - 1 m, equal to 0.1 m or 1 dm.

Explanation

The cistern's external dimensions are given as 3.3 m by 2.6 m by 1.1 m. From these dimensions, we can calculate the internal dimensions by subtracting twice the wall thickness from each external dimension. Since the walls are 5 cm thick, the internal dimensions would be 3.3 m - 0.1 m, 2.6 m - 0.1 m, and 1.1 m - 0.1 m. Simplifying these calculations, we get internal dimensions of 3.2 m, 2.5 m, and 1 m. The thickness of the bottom would be the difference between the external and internal height, which is 1.1 m - 1 m, equal to 0.1 m or 1 dm.

73. In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:

40 sec

47 sec

33 sec

None of These

In a 200 metres race, A beats B by 35 meters or 7 seconds. This means that A runs 200 meters in 7 seconds less than B. To find A's time over the course, we can calculate the time it takes for A to run 200 meters. If B takes 7 seconds to run 200 meters, then A must take 7 seconds less, which is 200 - 35 = 165 meters. Therefore, A's time over the course is 33 seconds.

Explanation

In a 200 metres race, A beats B by 35 meters or 7 seconds. This means that A runs 200 meters in 7 seconds less than B. To find A's time over the course, we can calculate the time it takes for A to run 200 meters. If B takes 7 seconds to run 200 meters, then A must take 7 seconds less, which is 200 - 35 = 165 meters. Therefore, A's time over the course is 33 seconds.

74. Select the lettered pair that has the same relationship as Sailor : Pirate

Police : Robbers

Lion : Lamb

Plant : Fungus

Major : Sepoy

The relationship between Sailor and Pirate is that a sailor is a person who works on a ship, while a pirate is a person who commits acts of robbery and violence at sea. Similarly, the relationship between Plant and Fungus is that a plant is a living organism that typically produces its own food through photosynthesis, while a fungus is a living organism that obtains nutrients by breaking down organic matter. Both pairs have a similar relationship of one entity being a type or category of the other.

Explanation

The relationship between Sailor and Pirate is that a sailor is a person who works on a ship, while a pirate is a person who commits acts of robbery and violence at sea. Similarly, the relationship between Plant and Fungus is that a plant is a living organism that typically produces its own food through photosynthesis, while a fungus is a living organism that obtains nutrients by breaking down organic matter. Both pairs have a similar relationship of one entity being a type or category of the other.

75. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

210

1050

25200

21400

None of these

To find the number of words that can be formed with 3 consonants and 2 vowels, we need to calculate the number of ways to choose the consonants and vowels separately, and then multiply those two numbers together.

The number of ways to choose 3 consonants out of 7 is given by the combination formula C(7, 3) = 7! / (3! * (7-3)!) = 35.

Similarly, the number of ways to choose 2 vowels out of 4 is given by C(4, 2) = 4! / (2! * (4-2)!) = 6.

Multiplying these two numbers together gives us 35 * 6 = 210.

However, this only gives us the number of ways to choose the letters, not the number of actual words that can be formed. Since the order of the letters matters, we need to consider the permutations as well.

There are 3 consonants, so there are 3! = 6 ways to arrange them. Similarly, there are 2 vowels, so there are 2! = 2 ways to arrange them.

Multiplying these two numbers together gives us 6 * 2 = 12.

Finally, multiplying the number of ways to choose the letters (210) by the number of ways to arrange them (12) gives us the total number of words that can be formed: 210 * 12 = 25200.

Therefore, the correct answer is 25200.

Explanation

To find the number of words that can be formed with 3 consonants and 2 vowels, we need to calculate the number of ways to choose the consonants and vowels separately, and then multiply those two numbers together.

The number of ways to choose 3 consonants out of 7 is given by the combination formula C(7, 3) = 7! / (3! * (7-3)!) = 35.

Similarly, the number of ways to choose 2 vowels out of 4 is given by C(4, 2) = 4! / (2! * (4-2)!) = 6.

Multiplying these two numbers together gives us 35 * 6 = 210.

However, this only gives us the number of ways to choose the letters, not the number of actual words that can be formed. Since the order of the letters matters, we need to consider the permutations as well.

There are 3 consonants, so there are 3! = 6 ways to arrange them. Similarly, there are 2 vowels, so there are 2! = 2 ways to arrange them.

Multiplying these two numbers together gives us 6 * 2 = 12.

Finally, multiplying the number of ways to choose the letters (210) by the number of ways to arrange them (12) gives us the total number of words that can be formed: 210 * 12 = 25200.

Therefore, the correct answer is 25200.

76. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

20

30

40

None of These

The given information states that the sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. To find the sum of the three numbers, we can set up a system of equations. Let the three numbers be a, b, and c. From the given information, we have the equations a^2 + b^2 + c^2 = 138 and ab + ac + bc = 131. By solving these equations, we find that a = 3, b = 4, and c = 5. Therefore, the sum of the three numbers is 3 + 4 + 5 = 12, which is not one of the given answer choices. Since none of the given answer choices is correct, the correct answer is None of These.

Explanation

The given information states that the sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. To find the sum of the three numbers, we can set up a system of equations. Let the three numbers be a, b, and c. From the given information, we have the equations a^2 + b^2 + c^2 = 138 and ab + ac + bc = 131. By solving these equations, we find that a = 3, b = 4, and c = 5. Therefore, the sum of the three numbers is 3 + 4 + 5 = 12, which is not one of the given answer choices. Since none of the given answer choices is correct, the correct answer is None of These.

77. The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount is:

RS 36

Rs 72

Rs 48

RS 96

The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount can be calculated by subtracting the banker's gain from the present worth. Therefore, the true discount is Rs. 576 - Rs. 16 = Rs. 560.

Explanation

The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount can be calculated by subtracting the banker's gain from the present worth. Therefore, the true discount is Rs. 576 - Rs. 16 = Rs. 560.

78. A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

400 M

450 M

560 M

600 M

The train completely crosses another train in 12 seconds, which means that the combined length of the two trains is covered in this time. Since the second train has half the length of the first train, the length of the first train can be calculated by multiplying the time taken to cross by the speed of the first train. Similarly, the length of the platform can be calculated by multiplying the time taken to pass the platform by the speed of the train. Therefore, the length of the platform is 48 kmph * 45 seconds = 2160 meters. Subtracting the length of the first train (48 kmph * 12 seconds = 576 meters) from the total length gives us the length of the platform, which is 2160 meters - 576 meters = 1584 meters. Since the length of the platform is given in meters, we need to convert it to kilometers, which gives us 1584 meters / 1000 = 1.584 kilometers. Finally, converting it back to meters, we get 1.584 kilometers * 1000 = 1584 meters, which is closest to 400 meters. Therefore, the correct answer is 400 M.

Explanation

The train completely crosses another train in 12 seconds, which means that the combined length of the two trains is covered in this time. Since the second train has half the length of the first train, the length of the first train can be calculated by multiplying the time taken to cross by the speed of the first train. Similarly, the length of the platform can be calculated by multiplying the time taken to pass the platform by the speed of the train. Therefore, the length of the platform is 48 kmph * 45 seconds = 2160 meters. Subtracting the length of the first train (48 kmph * 12 seconds = 576 meters) from the total length gives us the length of the platform, which is 2160 meters - 576 meters = 1584 meters. Since the length of the platform is given in meters, we need to convert it to kilometers, which gives us 1584 meters / 1000 = 1.584 kilometers. Finally, converting it back to meters, we get 1.584 kilometers * 1000 = 1584 meters, which is closest to 400 meters. Therefore, the correct answer is 400 M.

79. A train travelling at a speed of 75 mph enters a tunnel 31/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

2.5 MIN

3 MIN

3.2 MIN

3.5 MIN

The train is 1/4 mile long and the tunnel is 3 1/2 miles long. To calculate the time it takes for the train to pass through the tunnel, we need to find the total distance the train needs to cover. This is the sum of the length of the train and the length of the tunnel, which is 1/4 + 3 1/2 = 3 3/4 miles.

The train is traveling at a speed of 75 mph, so we can use the formula time = distance/speed to find the time it takes for the train to pass through the tunnel.

Time = (3 3/4) / 75 = 15/4 / 75 = 15/4 * 1/75 = 15/300 = 1/20 hours.

To convert this to minutes, we multiply by 60.

Time = (1/20) * 60 = 3 minutes.

Therefore, it takes 3 minutes for the train to pass through the tunnel.

Explanation

The train is 1/4 mile long and the tunnel is 3 1/2 miles long. To calculate the time it takes for the train to pass through the tunnel, we need to find the total distance the train needs to cover. This is the sum of the length of the train and the length of the tunnel, which is 1/4 + 3 1/2 = 3 3/4 miles.

The train is traveling at a speed of 75 mph, so we can use the formula time = distance/speed to find the time it takes for the train to pass through the tunnel.

Time = (3 3/4) / 75 = 15/4 / 75 = 15/4 * 1/75 = 15/300 = 1/20 hours.

To convert this to minutes, we multiply by 60.

Time = (1/20) * 60 = 3 minutes.

Therefore, it takes 3 minutes for the train to pass through the tunnel.

80. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:

4 days

5 days

6 days

7 days

The question states that 6 men and 8 boys can complete a piece of work in 10 days, while 26 men and 48 boys can complete the same work in 2 days. This implies that the work done by each man and boy is inversely proportional to the number of days taken to complete the work. So, if the number of men and boys is increased, the time taken to complete the work will decrease. Therefore, if there are 15 men and 20 boys, it will take less time than 10 days but more than 2 days. The closest option is 4 days, which is the correct answer.

Explanation

The question states that 6 men and 8 boys can complete a piece of work in 10 days, while 26 men and 48 boys can complete the same work in 2 days. This implies that the work done by each man and boy is inversely proportional to the number of days taken to complete the work. So, if the number of men and boys is increased, the time taken to complete the work will decrease. Therefore, if there are 15 men and 20 boys, it will take less time than 10 days but more than 2 days. The closest option is 4 days, which is the correct answer.

81. A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:

0%

5%

7.50%

10%

The man purchased the cow for Rs. 3000 and sold it for Rs. 3600 after giving the buyer a credit of 2 years. Since the buyer is given credit, it means that the payment will be made after 2 years. At an interest rate of 10% per annum, the amount after 2 years would be Rs. 3000 + (10% of Rs. 3000) = Rs. 3300. However, the man sold the cow for Rs. 3600, which is higher than the amount after 2 years. Therefore, there is no gain for the man, as he sold the cow for the same amount or less than what he would have received after 2 years with interest.

Explanation

The man purchased the cow for Rs. 3000 and sold it for Rs. 3600 after giving the buyer a credit of 2 years. Since the buyer is given credit, it means that the payment will be made after 2 years. At an interest rate of 10% per annum, the amount after 2 years would be Rs. 3000 + (10% of Rs. 3000) = Rs. 3300. However, the man sold the cow for Rs. 3600, which is higher than the amount after 2 years. Therefore, there is no gain for the man, as he sold the cow for the same amount or less than what he would have received after 2 years with interest.

82. Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:

Rs 4800

RS 50000

Rs 5400

Rs 5600

To have equal amounts of income from the investments in the 9% stock and the 10% stock, the total amount invested in each stock should be the same. Let the amount invested in the 9% stock be x. Therefore, the amount invested in the 10% stock would be (9800 - x). The income from the 9% stock would be (x * 9/100) and the income from the 10% stock would be ((9800 - x) * 10/100). Since the incomes are equal, we can set up the equation (x * 9/100) = ((9800 - x) * 10/100) and solve for x. By solving the equation, we find that x = 4800. Therefore, the investment in the 9% stock is Rs 4800.

Explanation

To have equal amounts of income from the investments in the 9% stock and the 10% stock, the total amount invested in each stock should be the same. Let the amount invested in the 9% stock be x. Therefore, the amount invested in the 10% stock would be (9800 - x). The income from the 9% stock would be (x * 9/100) and the income from the 10% stock would be ((9800 - x) * 10/100). Since the incomes are equal, we can set up the equation (x * 9/100) = ((9800 - x) * 10/100) and solve for x. By solving the equation, we find that x = 4800. Therefore, the investment in the 9% stock is Rs 4800.

83. In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

5.4 m

4.5 m

5 m

6 m

In the 100 m race, A beats B by 10 m and C by 13 m. This means that B is 3 m behind A in the 100 m race. Now, in the 180 m race, we can assume that B maintains the same speed as in the 100 m race. Therefore, B will cover an additional 80 m in the 180 m race. Since B is 3 m behind A in the 100 m race, B will now be 3 + 80 = 83 m behind A in the 180 m race. Given that B beat C by 13 m in the 100 m race, we can infer that B will beat C by the same margin in the 180 m race. Therefore, B will beat C by 13 m in the 180 m race, which is equivalent to 6 m.

Explanation

In the 100 m race, A beats B by 10 m and C by 13 m. This means that B is 3 m behind A in the 100 m race. Now, in the 180 m race, we can assume that B maintains the same speed as in the 100 m race. Therefore, B will cover an additional 80 m in the 180 m race. Since B is 3 m behind A in the 100 m race, B will now be 3 + 80 = 83 m behind A in the 180 m race. Given that B beat C by 13 m in the 100 m race, we can infer that B will beat C by the same margin in the 180 m race. Therefore, B will beat C by 13 m in the 180 m race, which is equivalent to 6 m.

84. Predict the output of the following code : main() { int i; for(i=0;i

1235689

123456789

12345678910

None of These

The code will output 123456789. This is because the for loop will iterate until the condition i

Explanation

The code will output 123456789. This is because the for loop will iterate until the condition i

85. . The output of the code below is #include int x; void main() { if (X) printf("hi"); else printf("how are u"); }

Hi

How are your

Compile time error

None of the mentioned

The output of the code is "how are you" because the condition in the if statement is checking the value of the variable "X". However, the variable "x" is not assigned any value before the if statement, so its value is undefined. Therefore, the condition in the if statement will evaluate to false and the code inside the else block will be executed, which is to print "how are you".

Explanation

The output of the code is "how are you" because the condition in the if statement is checking the value of the variable "X". However, the variable "x" is not assigned any value before the if statement, so its value is undefined. Therefore, the condition in the if statement will evaluate to false and the code inside the else block will be executed, which is to print "how are you".

86. How is the decimal value for 30 represented in binary?

00001111

00011010

00011110

00011111

The correct answer is 00011111. This is because in binary, each digit can be either 0 or 1. To represent the decimal value 30 in binary, we start from the leftmost digit and divide the number by 2 repeatedly, taking the remainder as the binary digit. In this case, 30 divided by 2 gives a quotient of 15 and a remainder of 0, so the rightmost digit is 0. Dividing 15 by 2 gives a quotient of 7 and a remainder of 1, so the next digit is 1. Continuing this process, we get 00011111 as the binary representation of 30.

Explanation

The correct answer is 00011111. This is because in binary, each digit can be either 0 or 1. To represent the decimal value 30 in binary, we start from the leftmost digit and divide the number by 2 repeatedly, taking the remainder as the binary digit. In this case, 30 divided by 2 gives a quotient of 15 and a remainder of 0, so the rightmost digit is 0. Dividing 15 by 2 gives a quotient of 7 and a remainder of 1, so the next digit is 1. Continuing this process, we get 00011111 as the binary representation of 30.