CAPF AC 2025 Q64: General Mental Ability – Quantitative Aptitude
If a/b = 2, b/c = 3, c/d = 4, d/e = 3, e/f = 2 and f/g = 1.5, what is the value of (a+b+c)/(e-f+g)?
- (a) 144
- (b) 216
- (c) 225
- (d) 120
Answer: (a) 144
Explanation
Chain of ratios
Given: a/b = 2, b/c = 3, c/d = 4, d/e = 3, e/f = 2, f/g = 1.5.
Find (a + b + c) / (e − f + g).
How to think: pick the last letter as g = 1 and work backwards through the ratios.
| Letter | Value | Working |
|---|---|---|
| g | 1 | chosen |
| f | 1.5 | f = 1.5 g |
| e | 3 | e = 2 f |
| d | 9 | d = 3 e |
| c | 36 | c = 4 d |
| b | 108 | b = 3 c |
| a | 216 | a = 2 b |
Numerator: a + b + c = 216 + 108 + 36 = 360.
Denominator: e − f + g = 3 − 1.5 + 1 = 2.5.
Value: 360 ÷ 2.5 = 144.
Bank key corrected: the stored key was (c) 225; the right answer is (a) 144.
Answer: (a) 144.
Why each option is right or wrong
- (a) CORRECT. The value is 360 ÷ 2.5, which is 144.
- (b) Incorrect. 216 is the value of a, not of the expression.
- (c) Incorrect. 225 does not follow from the chain of ratios.
- (d) Incorrect. 120 comes from a slip in the numerator or denominator.
Key point
Set g = 1: f = 1.5, e = 3, d = 9, c = 36, b = 108, a = 216. (a + b + c)/(e − f + g) = 360/2.5 = 144.
Remember
Start from the smallest letter g = 1 and multiply up the chain.
Common mistakes
- Using the first letter as 1 and getting fractions that are easy to mishandle.
- Writing e − f + g as e − (f + g), which changes the denominator.
- Dividing 360 by 2.5 wrongly (it is 144).
Exam tip
Educated guess: with g = 1 every letter is a clean number, and the denominator 2.5 divides 360 evenly. Only 144 and 216 are multiples that come from 360, and 216 is just a.
Sources
- NCERT Class VI Mathematics, Chapter 12 (Ratio and Proportion)
- NCERT Class VII Mathematics, Chapter 1 (Integers) and Chapter 2 (Fractions and Decimals: dividing by decimals)