Part VI — Numerical Aptitude

Chapter 7: Quantitative Aptitude Fundamentals

7.1 Percentages, Ratio and Proportion

Percentage expresses a number as a fraction of 100. Ratio compares two quantities of the same kind; proportion states that two ratios are equal. These form the foundation for many applied problem types (profit/loss, mixtures, partnerships).

7.2 Profit, Loss and Simple/Compound Interest

Profit/Loss is calculated relative to cost price (CP): Profit % = (Profit/CP) × 100. Simple Interest (SI) = (P×R×T)/100, where P is principal, R is annual rate, T is time in years. Compound Interest (CI) = P(1+R/100)ᵀ − P, reflecting interest earned on both principal and accumulated interest.

7.3 Time, Speed, Distance and Time & Work

Speed = Distance/Time. In relative motion problems, speeds add when moving toward each other and subtract when moving in the same direction. Time & Work problems use the principle that work done is inversely proportional to time taken, with combined work rates adding when multiple agents work together.

7.4 Data Interpretation

Data Interpretation (DI) questions test the ability to read and analyse data presented in tables, bar graphs, line graphs, and pie charts, then perform calculations (percentages, ratios, averages) based on that data.

7.5 Practice Set — Quantitative Aptitude (16 MCQs)

1. What is 25% of 480?
   (a) 100 (b) 110 (c) 120 (d) 130
2. If the ratio of two numbers is 3:5 and their sum is 64, the smaller number is:
   (a) 20 (b) 24 (c) 28 (d) 32
3. A shopkeeper buys an item for ₹800 and sells it for ₹960. His profit percentage is:
   (a) 15% (b) 20% (c) 25% (d) 30%
4. The simple interest on ₹5000 at 8% per annum for 3 years is:
   (a) ₹1000 (b) ₹1100 (c) ₹1200 (d) ₹1300
5. A train covers 300 km in 5 hours. Its average speed is:
   (a) 50 km/h (b) 60 km/h (c) 70 km/h (d) 75 km/h
6. Two trains, 150 km apart, move toward each other at 60 km/h and 40 km/h respectively. They will meet after:
   (a) 1 hour (b) 1.5 hours (c) 2 hours (d) 2.5 hours
7. A can complete a work in 10 days, B in 15 days. Working together, they will complete the work in:
   (a) 5 days (b) 6 days (c) 8 days (d) 12 days
8. If A's income is 25% more than B's, then B's income is what percent less than A's?
   (a) 20% (b) 25% (c) 30% (d) 15%
9. The compound interest on ₹10,000 at 10% per annum for 2 years (compounded annually) is:
   (a) ₹2,000 (b) ₹2,100 (c) ₹2,200 (d) ₹1,900
10. In a mixture, milk and water are in the ratio 4:1. If the total mixture is 50 litres, the quantity of water is:
    (a) 8 litres (b) 10 litres (c) 12 litres (d) 15 litres
11. A sum of ₹6000 is divided among A, B, and C in the ratio 2:3:1. B's share is:
    (a) ₹1000 (b) ₹2000 (c) ₹3000 (d) ₹4000
12. If the marked price of an item is ₹1000 and a discount of 20% is given, the selling price is:
    (a) ₹700 (b) ₹750 (c) ₹800 (d) ₹850
13. In a pie chart representing total sales, a sector of 90° represents what fraction of total sales?
    (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6
14. A boat's speed in still water is 10 km/h, and the current's speed is 2 km/h. The boat's downstream speed is:
    (a) 8 km/h (b) 10 km/h (c) 12 km/h (d) 14 km/h
15. If 5 workers can build a wall in 12 days, how many days will 10 workers take (assuming the same work rate per worker)?
    (a) 4 days (b) 6 days (c) 8 days (d) 10 days
16. The average of 5 consecutive integers starting from 10 is:
    (a) 10 (b) 11 (c) 12 (d) 13

Answer Key

1.(c)

2.(b)

3.(b)

4.(c)

5.(b)

6.(b)

7.(b)

8.(a)

9.(b)

10.(b)

11.(c)

12.(c)

13.(c)

14.(c)

15.(b) 16.(c)