"Quantitative Aptitude" — Practice

Question 1

The price of an item increases by 25 per cent. By what percentage must it now be reduced to return to the original price?

Accepted Answer

B

Question 2

A can complete a task in 15 days and B in 10 days. Working together, how many days do they take?

Accepted Answer

A

Question 3

Two numbers are in the ratio 5 : 8 and their sum is 143. What is the larger number?

Accepted Answer

B

Question 4

In what ratio must a shopkeeper mix tea costing 180 rupees per kg with tea costing 300 rupees per kg to obtain a mixture worth 220 rupees per kg?

Accepted Answer

Use alligation. The distances from the mean are what matter, and the quantities come out in the inverse ratio of those distances.

Distance of the cheaper from the mean: 220 - 180 = 40.
Distance of the dearer from the mean: 300 - 220 = 80.

The ratio of quantities is the inverse of these distances, so cheaper to dearer is 80 : 40 = 2 : 1.

Check it directly: taking 2 kg at 180 and 1 kg at 300 gives 360 + 300 = 660 rupees for 3 kg, which is 220 per kg.

The reason the ratio is inverted is that the component nearer the mean must be present in greater quantity to pull the average towards itself.

Question 5

A train 180 m long travelling at 54 km/h crosses a platform in 20 seconds. What is the length of the platform, in metres?

Accepted Answer

Convert the speed to metres per second: 54 km/h times 5/18 gives 15 m/s.

When a train crosses a platform, the distance covered is the length of the train plus the length of the platform, because the rear of the train must clear the far end of the platform.

Distance covered in 20 seconds at 15 m/s is 300 m.

So 180 + P = 300, giving P = 120 metres.

The standard error is to use only the platform length, which would be correct for a point object but not for a train of finite length. Crossing a pole, by contrast, covers only the train's own length.

Question 6

A committee of 3 is to be chosen from 5 engineers and 4 managers, with at least one manager. In how many ways can this be done?

Accepted Answer

Count the complement, since the condition is an at-least condition.

Total ways to choose any 3 from the 9 people: C(9,3) = 84.

Ways to choose 3 with no manager, meaning all three from the 5 engineers: C(5,3) = 10.

Ways with at least one manager: 84 - 10 = 74.

The direct route would require adding three cases — exactly one, exactly two and exactly three managers — giving 4 times C(5,2) plus C(4,2) times 5 plus C(4,3), which is 40 + 30 + 4 = 74. The same answer, three times the work.

Whenever a condition is phrased as at least one, counting what is forbidden and subtracting is faster and less error-prone.

Question 7

A trader sells two articles at 960 rupees each. On one he gains 20 per cent and on the other he loses 20 per cent. What is his overall profit or loss percentage?

Accepted Answer

The two do not cancel, because the equal percentages are taken on different cost prices.

For the article sold at a 20 per cent gain, the cost price is 960/1.2 = 800.
For the article sold at a 20 per cent loss, the cost price is 960/0.8 = 1200.

Total cost is 2000 and total selling price is 1920, so the loss is 80 on 2000, which is 4 per cent.

The general result is a net loss of x squared over 100 per cent, and here 20 squared over 100 gives exactly 4 per cent.

The result is independent of the selling price, which is why the formula can be applied without computing the cost prices at all. What makes the intuition fail is that the loss is taken on the larger cost price and the gain on the smaller, so the loss in rupees always exceeds the gain.

Question 8

A vessel contains 81 litres of pure milk. 27 litres are drawn off and replaced with water. This is repeated twice more. What is the ratio of milk to water in the final mixture?

Accepted Answer

Each operation removes a fixed fraction of what is present rather than a fixed quantity of milk, because after the first step the liquid drawn off already contains water.

The fraction removed each time is 27/81 = 1/3, so the milk remaining is multiplied by 2/3 at each step.

After three operations the milk is 81 times (2/3) cubed = 81 times 8/27 = 24 litres.

The vessel still holds 81 litres in total, so the water is 81 - 24 = 57 litres.

The ratio of milk to water is 24 : 57 = 8 : 19.

The error worth avoiding is computing 81 - 3(27) = 0, which would be correct only if each removal took 27 litres of pure milk. It does not, and by the third operation more than a third of what is drawn off is water.

Question 9

A company's revenue was 480 crore in 2019, 552 crore in 2020, 621 crore in 2021 and 745.2 crore in 2022. In which year was the percentage growth over the previous year the highest?

Accepted Answer

Compute each growth against the previous year's value as base, and note that the absolute increases are misleading because the base rises every year.

2020 over 2019: increase 72 on 480, which is 72/480 = 15 per cent.

2021 over 2020: increase 69 on 552, which is 69/552 = 12.5 per cent.

2022 over 2021: increase 124.2 on 621, which is 124.2/621 = 20 per cent.

The highest percentage growth is in 2022, at 20 per cent.

Two observations make this fast. First, 2021 has both a smaller absolute increase and a larger base than 2020, so it can be eliminated without dividing. Second, the comparison between 2020 and 2022 can be settled by noting that 124.2 is more than a fifth of 621 while 72 is less than a fifth of 480, again without exact division.

Practice — "Quantitative Aptitude"

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