IGCSE Math B May'21 Batch Online Quiz On Arithmetic

1.

On a journey of 960 kilometers, David’s car used 91 liters of petrol. Given that 4.55 liters = 1 gallon, Calculate the number of kilometer per gallon that David’s car used on the journey.

A.

48 kilometer per gallon
B.

45.7 kilometer per gallon
C.

70.23 kilometer per gallon
D.

25.3 kilometer per gallon

Correct Answer
A. 48 kilometer per gallon

Explanation
To calculate the number of kilometers per gallon, we need to convert the liters of petrol used into gallons. Since 4.55 liters is equal to 1 gallon, we divide the given number of liters (91) by 4.55 to get the number of gallons used (20).

Next, we divide the total distance traveled (960 kilometers) by the number of gallons used (20) to get the number of kilometers per gallon.

960 kilometers divided by 20 gallons equals 48 kilometers per gallon. Therefore, the correct answer is 48 kilometers per gallon.

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2.

The distance between two features on a photo is 11.5 cm and the corresponding distance is 5 km on the ground. What is the approximate scale of the photo? Answer Format= ( Photo length: Real length)

A.

32 : 100000000
B.

27 : 10000
C.

23 : 1000000
D.

1000000 : 24

Correct Answer
C. 23 : 1000000

Explanation
The scale of the photo can be calculated by dividing the distance between the two features on the photo (11.5 cm) by the corresponding distance on the ground (5 km). This gives us a scale of approximately 0.0023 cm per meter or 23 : 1000000.

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3.

N taka is shared between three person in the ratio 2:3:7. The largest share is 540 taka more than the smallest share. Calculate the value of N.

A.

1692
B.

3217
C.

2000
D.

1296

Correct Answer
D. 1296

Explanation
The ratio of the shares is 2:3:7. Let the smallest share be x taka. The largest share is 540 taka more than the smallest share, so it is x + 540 taka. The total sum of the shares is N taka. From the ratio, we can set up the equation 2x + 3x + 7x = N. Simplifying, we get 12x = N. Since the largest share is 540 taka more than the smallest share, we can also set up the equation x + 540 = 7x. Solving this equation, we get x = 90 taka. Substituting this value into the equation 12x = N, we get N = 12 * 90 = 1080 taka. However, this value is not among the answer choices. So, we need to check the other answer choices. The only answer choice that satisfies the condition that the largest share is 540 taka more than the smallest share is 1296 taka. Therefore, the value of N is 1296 taka.

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4.

Cost Price Selling Price Profit (%) Loss (% ) $2400 25.5 % $1900 36 % $2950 10% $2980 $2590 % $4100 25% $650 $800 % $41650 28% $71580 $68340 % $690 75% $890500 $1996000 % Fill the answers. You must give the answers in 1 decimal place.

Correct Answer
3012
1216
2682
13.1
5125
23.1
57847.2
4.5
394.3
124.1

5.

Two brothers, Abraham and Ibrahim , set off for their school one day. Abraham left home at 07:17 and walked to school, arriving at 08:32. Ibrahim left home at 08:21 and cycled to school arriving at 08:46. Calculate the ratio of Abraham’s journey time : Ibrahim’s journey time, giving your answer in the form n:1.

A.

2 : 5
B.

1 : 3
C.

5 : 2
D.

3 : 1

Correct Answer
D. 3 : 1

Explanation
Abraham's journey time can be calculated by subtracting his departure time from his arrival time: 08:32 - 07:17 = 1 hour and 15 minutes. Ibrahim's journey time can be calculated in the same way: 08:46 - 08:21 = 25 minutes. To find the ratio of their journey times, we convert the times to a common unit, such as minutes. Abraham's journey time is 75 minutes and Ibrahim's journey time is 25 minutes. Therefore, the ratio of Abraham's journey time to Ibrahim's journey time is 3:1.

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6.

Given that x : y = 6 : 5 and y : z = 4 : 5, find the ratio x:y:z in integer form.

A.

7 : 6 : 9
B.

24 : 20 : 25
C.

6 : 5 : 4
D.

25 : 20 : 24

Correct Answer
B. 24 : 20 : 25

Explanation
The ratio x:y:z can be found by multiplying the given ratios x:y and y:z. By doing this, we get (6/5) * (4/5) = 24/25. Therefore, the ratio x:y:z is 24 : 20 : 25.

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7.

In a country, the number of people who are more than 60 years old is 23% of the population. Of these people who are more than 60 years old, 42% are men. The population of the country is 50 million. Calculate, to the nearest million, the number of women in this country who are more than 60 years old.

A.

7 million
B.

5 million
C.

8 million
D.

6 million

Correct Answer
A. 7 million

Explanation
23% of the population is more than 60 years old, which means there are 0.23 * 50 million = 11.5 million people who are more than 60 years old. Of these, 42% are men, so the number of men who are more than 60 years old is 0.42 * 11.5 million = 4.83 million. Therefore, the number of women who are more than 60 years old is 11.5 million - 4.83 million = 6.67 million. Rounding to the nearest million gives us 7 million women.

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8.

A new car is tested by timing how long it took to travel a distance of 1.7 km. On the first test drive the car’s average speed was 113.2 km/h. On second test drive the car took exactly 53s to cover the distance. Find the difference in 1 decimal place, in km/h, between the average speeds of the two test drives.

A.

80 km/h
B.

Option 2
C.

2.3 km/h
D.

114.9 km/h

Correct Answer
C. 2.3 km/h

Explanation
The difference in average speeds between the two test drives can be found by subtracting the average speed of the first test drive from the average speed of the second test drive.

For the first test drive, the average speed is given as 113.2 km/h.

For the second test drive, the time taken to cover the distance is given as 53s. To convert this to hours, we divide by 3600 (since there are 3600 seconds in an hour). This gives us a time of 0.0147 hours.

To find the average speed for the second test drive, we divide the distance of 1.7 km by the time of 0.0147 hours. This gives us an average speed of approximately 115.6 km/h.

Finally, we subtract the average speed of the first test drive (113.2 km/h) from the average speed of the second test drive (115.6 km/h) to find the difference in average speeds, which is approximately 2.3 km/h.

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9.

Sonia works in a shop. She is paid $7.60 per hour she works. She is also paid 4% of the value of the items she sells in a week.

In one week she works for 36 hours and the value of the item she sells is $4250. Sonia’s total pay for that week is .

In another week Sonia worked for 41 hours and the total pay for that week was $430.80. The value of the items Sonia sells this week was . (DO NOT USE $ SIGN)

Correct Answer
443.6
2980

Explanation
In the first week, Sonia worked for 36 hours and the value of the items she sold was $4250. Her total pay for that week can be calculated by multiplying her hourly rate of $7.60 by the number of hours worked (36) and then adding 4% of the value of the items sold ($4250 * 0.04). This gives us a total pay of $273.60 + $170 = $443.60.

In the second week, the total pay was given as $430.80. We are asked to find the value of the items Sonia sold that week. To do this, we need to subtract the amount she earned from working (41 hours * $7.60) from the total pay ($430.80). This gives us $430.80 - $311.60 = $119.20. Since the answer format does not include a dollar sign, the value of the items Sonia sold that week is 2980.

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4

10.

Emi invested an amount of money for 3 years in a savings account. At the end of each year interest was added to her account. At the end of the first year 5.1% interest was added to the account. At the end of the second year the interest added was 4.5% of the amount in the account. At the end of the final year the interest added was 4.5% of the amount in the account. At the end of the 3 year the amount in account was $2123.28 Calculate the amount of money that Sonia invested. Give your answer to the nearest $.

A.

$1851
B.

$1800
C.

$1900
D.

$2000

Correct Answer
A. $1851

Explanation
To find the amount of money that Sonia invested, we need to work backwards from the final amount of $2123.28. We know that at the end of the first year, 5.1% interest was added to the account. So, the amount at the end of the first year can be calculated by dividing $2123.28 by 1.051. This gives us $2019.27.

Now, at the end of the second year, 4.5% interest was added to the account. So, the amount at the end of the second year can be calculated by dividing $2019.27 by 1.045. This gives us $1930.48.

Finally, at the end of the third year, 4.5% interest was added to the account. So, the amount at the end of the third year can be calculated by dividing $1930.48 by 1.045. This gives us $1850.95, which rounds to $1851.

Therefore, the amount of money that Sonia invested is $1851.

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