Ibps Quantitative Ability Test 1

Explanation
The shopkeeper earns a profit of 12% on selling the book, which means that the selling price is 112% of the cost price. The book is sold at a 10% discount on the printed price, so the selling price is 90% of the printed price. This implies that 112% of the cost price is equal to 90% of the printed price. Simplifying this equation, we find that the ratio of the cost price to the printed price is 45:56.

Explanation
The ratio of boys to girls in the school is 3:2. This means that for every 3 boys, there are 2 girls. Let's assume there are 5 students in total (3 boys and 2 girls). If 20% of the boys are scholarship holders, then 20% of 3 boys is 0.6 boys. Similarly, if 25% of the girls are scholarship holders, then 25% of 2 girls is 0.5 girls. So, the total number of scholarship holders is 0.6 boys + 0.5 girls = 1.1 students. The percentage of students who are not scholarship holders is (5 - 1.1)/5 * 100 = 78%.

Explanation
A does half as much work as B, which means that if B does 1 unit of work, A does 0.5 units of work. C does half as much work as A and B together, so if A and B together do 1 unit of work, C does 0.5 units of work. If C alone can finish the work in 12 days, it means that in 1 day, C does 1/12 units of work. Therefore, in 1 day, A and B together do 1 unit of work and C does 1/12 units of work. So, together all will finish the work in 12/(1+1/12) = 7 days.

Explanation
Since tap A can fill the bucket in 12 minutes and tap B can fill it in 15 minutes, we can calculate their rates of filling the bucket.

Tap A fills 1/12 of the bucket per minute, while tap B fills 1/15 of the bucket per minute.

When both taps are opened, their combined rate of filling the bucket is 1/12 + 1/15 = 9/60 = 3/20 of the bucket per minute.

After 3 minutes, tap A is closed, so only tap B is filling the bucket at a rate of 1/15 of the bucket per minute.

To find out how much further time it would take for B to fill the bucket, we need to calculate the remaining amount of the bucket that B needs to fill.

In 3 minutes, the combined rate of A and B filled 3/20 * 3 = 9/20 of the bucket.

Therefore, the remaining amount of the bucket that B needs to fill is 1 - 9/20 = 11/20 of the bucket.

Since B fills 1/15 of the bucket per minute, it would take B (11/20) / (1/15) = 165/20 = 8 mm. 15 sec to fill the remaining amount of the bucket.

Hence, the correct answer is 7 mm. 45 sec.

Explanation
The train is passing a man running in the opposite direction, so their speeds should be added. The length of the train is given as 110 m, and the time taken to pass the man is given as 6 seconds. To find the speed of the train, we can use the formula speed = distance/time. The distance covered by the train in 6 seconds is 110 m, and the speed of the man is given as 6 km/hr, which is equivalent to 6 * 1000/3600 m/s. Adding the speeds of the train and the man, we can calculate the speed of the train as 110/6 + 6 * 1000/3600 m/s. Converting this to km/hr, we get the answer as 60 km/hr.

Explanation
The boat's speed in still water is 4 kmph, and the stream's velocity is 2 kmph. When the boat travels downstream, it gains the stream's velocity, so its effective speed is 6 kmph. When it travels upstream, it subtracts the stream's velocity, so its effective speed is 2 kmph. Since the boat takes the same amount of time for both trips, the distance between A and B must be the same as the time it takes to travel, which is 6 km.

Explanation
The man covered a total distance of 2000 km in 18 hours. Let's assume he covered x km by bus. The remaining distance, which is (2000 - x) km, must have been covered by train. The time taken to cover the distance by bus is x/72 hours, and the time taken to cover the distance by train is (2000 - x)/160 hours. Since the total time taken is 18 hours, we can set up the equation x/72 + (2000 - x)/160 = 18. Solving this equation, we find x = 720 km. Therefore, the distance covered by bus is 720 km.

Explanation
The least perfect square number that is divisible by 3, 4, 5, 6, and 8 is 3600. This is because 3600 is the smallest number that can be divided evenly by all the given numbers and is also a perfect square.