Quantitative aptitude for placement tests: 12 questions solved

Percentages and money

1. A price rises by 20% and then falls by 20%. What is the net change?

Shortcut: two successive changes of +a% and −b% multiply as (1 + a)(1 − b). Here 1.20 × 0.80 = 0.96. Full working: start at ₹100. After the rise, ₹120. A 20% fall on ₹120 is ₹24, leaving ₹96. Answer: a 4% decrease. The common wrong answer is "no change".

2. Successive discounts of 10% and 15% equal what single discount?

0.90 × 0.85 = 0.765, so you pay 76.5% of the price. Answer: 23.5%, not 25%.

3. An article costs ₹800. The shop marks it 25% above cost and then gives a 10% discount. Find the profit percentage.

Marked price = 800 × 1.25 = ₹1,000. Selling price = 1,000 × 0.90 = ₹900. Profit = ₹100 on a cost of ₹800. Answer: 12.5%. Profit percentage is always on cost unless the question says otherwise.

4. What is the difference between compound and simple interest on ₹10,000 at 10% a year for 2 years?

Simple interest = 10,000 × 0.10 × 2 = ₹2,000. Compound amount = 10,000 × 1.1 × 1.1 = ₹12,100, so compound interest = ₹2,100. Answer: ₹100. Shortcut for 2 years: difference = P × r², here 10,000 × 0.01 = ₹100.

Ratios and mixtures

5. A:B = 3:4 and B:C = 6:5. Find A:B:C.

Make B the same in both. The LCM of 4 and 6 is 12. A:B = 9:12 and B:C = 12:10. Answer: 9:12:10.

6. A 40-litre mixture has milk and water in the ratio 3:1. How much water must be added to make the ratio 3:2?

Milk = 30 L, water = 10 L. Milk does not change, so for 3:2 water must be 30 × 2/3 = 20 L. Answer: add 10 litres.

Rates: work, pipes and speed

7. A finishes a job in 12 days and B in 18 days. How long together?

Work per day: 1/12 + 1/18 = 3/36 + 2/36 = 5/36. Time = 36/5. Answer: 7.2 days (7 days and a fifth of a day).

8. One pipe fills a tank in 10 hours and another empties it in 15 hours. Both are opened together on an empty tank. When is it full?

Net rate = 1/10 − 1/15 = 3/30 − 2/30 = 1/30. Answer: 30 hours.

9. A 180 m train passes a pole in 9 seconds. How long does it take to cross a 270 m platform?

Speed = 180/9 = 20 m/s (that is 72 km/h, since 20 × 18/5 = 72). To cross a platform the train covers its own length plus the platform: 180 + 270 = 450 m. Time = 450/20. Answer: 22.5 seconds.

Averages

10. The average of five numbers is 42. When one number is removed, the average of the remaining four is 40. What was removed?

Total of five = 5 × 42 = 210. Total of four = 4 × 40 = 160. Answer: 50. Averages questions almost always become totals questions.

Probability and counting

11. Two fair dice are thrown. What is the probability that the sum is 7?

Favourable pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — six of 36. Answer: 1/6.

12. In how many ways can the letters of LEVEL be arranged?

Five letters with L twice and E twice: 5! / (2! × 2!) = 120 / 4. Answer: 30.

Check your own answers with a script

When you make your own practice questions, you need an answer key you trust. This short Python script recomputes all twelve answers above using exact fractions. It uses only the standard library.

from fractions import Fraction as F
from itertools import permutations, product

answers = {
    1: (F(120, 100) * F(80, 100) - 1) * 100,          # net % change
    2: (1 - F(90, 100) * F(85, 100)) * 100,           # single discount %
    3: (800 * F(125, 100) * F(90, 100) - 800) / 800 * 100,
    4: 10000 * F(11, 10) ** 2 - 10000 - 10000 * F(10, 100) * 2,
    6: 30 * F(2, 3) - 10,                             # litres of water to add
    7: 1 / (F(1, 12) + F(1, 18)),                     # days
    8: 1 / (F(1, 10) - F(1, 15)),                     # hours
    9: (180 + 270) / F(180, 9),                       # seconds
    10: 5 * 42 - 4 * 40,
    11: F(sum(1 for a, b in product(range(1, 7), repeat=2) if a + b == 7), 36),
    12: len(set(permutations("LEVEL"))),
}
for q, value in answers.items():
    print(q, value, float(value))

Question 5 is a ratio rather than a number, so check it by hand: 9/12 = 3/4 and 12/10 = 6/5. The script prints −4 for question 1 (a decrease), 47/2 for question 2 (23.5), 25/2 for question 3, 100 for question 4, 10, 36/5, 30, 45/2, 50, 1/6 and 30.

How to practise so it transfers to the test

• Do topics in blocks of 15 questions for the first two weeks, then switch to mixed sets, because the real test does not tell you the topic.
• Time every set. Write the time next to each question and look for types where you are slow rather than wrong.
• Keep an error log with three columns: question type, what you did, what the relationship actually is. Revise the log, not the textbook, in the last week.

Aptitude sections usually sit alongside logical and verbal ones; our logical reasoning patterns guide covers the next section. The arithmetic habits here — checking a total, questioning a percentage base — are also the first things taught in the Data Analyst programme, because they are what stops a wrong number reaching a dashboard.