CAPF AC 2020 Q113: General Mental Ability – Quantitative Aptitude
If 15% of A is double of 30% of B, then what is the ratio of A to B?
- (a) 1 : 2
- (b) 2 : 1
- (c) 1 : 4
- (d) 4 : 1
Answer: (d) 4 : 1
Explanation
Ratio from percentages
Given: 15% of A is double of 30% of B.
We need the ratio of A to B.
How to think: write the sentence as an equation.
Double of 30% is 60%.
So 15% of A equals 60% of B.
| Step | Working |
|---|---|
| Equation | 15% of A = 2 × 30% of B |
| Simplify | 15 × A = 60 × B |
| Divide | A ÷ B = 60 ÷ 15 = 4 |
| Ratio | A : B = 4 : 1 |
Check with numbers: take B = 100 and A = 400.
15% of 400 is 60.
30% of 100 is 30, and double of it is 60.
Both sides match.
Sense check: a smaller percentage of A equals a bigger percentage of B.
So A must be the larger number.
Answer: (d) 4 : 1.
Why each option is right or wrong
- (a) Incorrect. 1 : 2 makes A smaller than B, but A must be larger.
- (b) Incorrect. 2 : 1 misses the word double; it only compares 15% with 30%.
- (c) Incorrect. 1 : 4 is the ratio upside down, B to A.
- (d) CORRECT. 15A = 60B, so A : B = 4 : 1.
Key point
x% of A = y% of B gives A : B = y : x. Here 15% of A = 60% of B, so A : B = 60 : 15 = 4 : 1.
Remember
x% of A = y% of B means A : B = y : x.
Common mistakes
- Missing the word double and getting 2 : 1.
- Writing the ratio upside down as 1 : 4.
- Doubling the wrong side, the 15% instead of the 30%.
Exam tip
Educated guess: a small share of A matches a big share of B, so A is bigger. That removes (a) and (c).
Sources
- NCERT Class VII Mathematics — Comparing Quantities (percentage and ratio)
- NCERT Class VIII Mathematics — Comparing Quantities