Ibps Quantitative Ability Test 1

1) The 1east perfect square number which is divisible by 3, 4, 5, 6,and 8 is—

900

1600

2500

3600

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.

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.

2) A man covered a-distance of 2000 km in 18 hours partly by bus at 72 kmph and partly by train at 160 kmph. The distance covered by bus is—.

860 km

640 km

1280 km

720 km

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 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.

3) The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, the percentage of the school students who are not scholarship holders, is—

78

80

56

70

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

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%.

4) A boat takes 4 hours for travelling downstream from point A to point B and coming back to point A upstream. If the velocity of the stream is 2 kmph and the speed of the boat in still water is 4 kmph, whit is the distance between A and B?

8 km

9 km

4 km

6 km

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 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.

5) A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price to the printed price of the book is—

99 : 125

55 : 69

50: 61

45 : 56

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 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.

6) Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes, how much further time would it take for B to fill the bucket?

8 mm. 5 sec

8 mm. 25 sec

7 mm. 45 sec

7 mm. 15 sec

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

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.

7) A train -110 m long passes a man, running at 6 kmph in the direction opposite to that of the train in 6 seconds. The speed of the train is—

54 km/hr

72 km/hr

60 km/hr

66 km/hr

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 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.

8) The difference between simple interest and compound. Interest on Rs. 1200 for one year at 10% per annum, reckoned half yearly is—

Rs. 8.80

Rs. 3

Nil

Rs. 13.20

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Explanation

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9) When simplified, the product (2 – 1/2) (2 – 3/5) (2- 5/7)…….(2 -997/999) is equal to

5/999

1001/999

1001 /3

None of these

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Explanation

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10) A does half as much work as B and C does half as much work as A and B together. If C alone can finish the work in 12 days, then together all will finish the work in—

6 days

7 days

4 days

5 days

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

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.