CAPF AC 2020 Q116: General Mental Ability – Quantitative Aptitude
- (a) 20 years
- (b) 30 years
- (c) 40 years
- (d) 50 years
Answer: (a) 20 years
Explanation
Compound interest: triple, then nine times
Given: a sum triples in ten years under compound interest, compounded annually.
We need the number of years in which it becomes nine times.
How to think: under compound interest, the sum is multiplied by the same factor in every equal period.
Here the factor is 3 for every 10 years.
Nine is 3 × 3, so two such periods are needed.
| Years | Amount |
|---|---|
| 0 | P |
| 10 | 3P |
| 20 | 3 × 3P = 9P |
| 30 | 3 × 9P = 27P |
By formula: (1 + r)¹⁰ = 3.
Squaring both sides, (1 + r)²⁰ = 9.
So the time is 20 years.
Compare with simple interest:
| Type | Triples in 10 years, nine times in |
|---|---|
| Compound interest | 20 years |
| Simple interest | 40 years (interest of 2P per 10 years; 8P needed) |
Answer: (a) 20 years.
Why each option is right or wrong
- (a) CORRECT. Tripling twice gives nine times, so it takes 10 + 10 = 20 years.
- (b) Incorrect. In 30 years the sum becomes 27 times.
- (c) Incorrect. 40 years is the answer under simple interest.
- (d) Incorrect. 50 years fits neither kind of interest.
Key point
Compound interest: if a sum becomes n times in t years, it becomes n² times in 2t years and n³ times in 3t years.
Remember
Compound interest: n times in t years means n² times in 2t years.
Common mistakes
- Using the simple interest idea and marking 40 years.
- Thinking nine times needs three periods because 9 ÷ 3 = 3.
- Trying to find the rate first; it is not needed.
Exam tip
Educated guess: compound interest multiplies. Three times, then three times again, is nine times: two periods.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities (compound interest)
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Compound Interest)