Part VI — Numerical Ability

Chapter 6: Arithmetic, Algebra & Geometry

6.1 Percentage, Profit & Loss, and Interest

Percentage conversions form the basis for comparing quantities. Profit and loss: Profit % = (Profit/Cost Price) × 100. Simple Interest = (Principal × Rate × Time)/100; Compound Interest = Principal × [(1 + Rate/100)ᵀ − 1].

6.2 Time, Speed, Distance, and Averages

Time and distance: Speed = Distance/Time. Averages = Sum of observations / Number of observations, frequently combined with time-distance problems (average speed over a journey with varying speeds).

6.3 Algebra

Basic linear equations and simple quadratic equations form the algebra component, generally at a moderate difficulty level.

6.4 Trigonometry and Geometry

Basic trigonometric ratios (sine, cosine, tangent for standard angles) and geometry covering areas/perimeters of standard shapes (triangles, circles, rectangles) and volumes of standard solids (cubes, cylinders, spheres) round out this section.

6.5 Statistics Basics

Basic statistics concepts — mean, median, and mode of small data sets — are occasionally tested alongside averages.

6.6 Practice Set — Numerical Ability (15 MCQs)

1. A shopkeeper buys an item for ₹600 and sells it for ₹750. What is the profit percentage?
   (a) 20% (b) 25% (c) 22% (d) 30%
2. Find the simple interest on ₹4000 at 6% per annum for 5 years.
   (a) ₹1000 (b) ₹1100 (c) ₹1200 (d) ₹1300
3. Find the compound interest on ₹5000 at 10% per annum for 2 years, compounded annually.
   (a) ₹1000 (b) ₹1050 (c) ₹1100 (d) ₹950
4. A train travels 240 km in 4 hours. What is its average speed?
   (a) 50 km/h (b) 55 km/h (c) 60 km/h (d) 65 km/h
5. The average of 4 numbers is 25. If a 5th number is added, the average becomes 27. What is the 5th number?
   (a) 33 (b) 35 (c) 37 (d) 39
6. Solve for x: 3x + 7 = 2x + 15.
   (a) 6 (b) 7 (c) 8 (d) 9
7. If x² − 5x + 6 = 0, the values of x are:
   (a) 2 and 3 (b) 1 and 6 (c) −2 and −3 (d) 4 and 1
8. What is the value of sin 30°?
   (a) 1/2 (b) 1 (c) 0 (d) √3/2
9. What is the value of cos 60°?
   (a) 1/2 (b) 1 (c) 0 (d) √3/2
10. Find the area of a triangle with base 10 cm and height 8 cm.
    (a) 30 sq cm (b) 40 sq cm (c) 45 sq cm (d) 50 sq cm
11. Find the circumference of a circle with radius 14 cm (use π = 22/7).
    (a) 84 cm (b) 88 cm (c) 92 cm (d) 96 cm
12. Find the volume of a cylinder with radius 7 cm and height 10 cm (use π = 22/7).
    (a) 1400 cubic cm (b) 1470 cubic cm (c) 1540 cubic cm (d) 1610 cubic cm
13. Find the mean of the data set: 4, 8, 6, 10, 12.
    (a) 7 (b) 8 (c) 9 (d) 10
14. Find the median of the data set: 3, 7, 9, 15, 21.
    (a) 7 (b) 9 (c) 15 (d) 12
15. A car covers the first half of a journey at 40 km/h and the second half at 60 km/h. What is the average speed for the whole journey?
    (a) 48 km/h (b) 50 km/h (c) 52 km/h (d) 45 km/h

Answer Key

1.(b)

2.(c)

3.(b)

4.(c)

5.(b)

6.(c)

7.(a)

8.(a)

9.(a)

10.(b)

11.(b)

12.(c)

13.(b)

14.(b) 15.(a)