CAPF AC 2021 Q96: General Mental Ability – Quantitative Aptitude
- (a) ₹1,00,000
- (b) ₹80,000
- (c) ₹40,000
- (d) ₹1,20,000
Answer: (a) ₹1,00,000
Explanation
Difference between compound and simple interest for two years
Given: the difference between compound interest and simple interest at 5% per year for 2 years is ₹250; find the sum.
How to think: for two years the difference is just the interest on the first year's interest.
That gives a short formula.
| Step | Working |
|---|---|
| Formula for 2 years | Difference = P × (R/100)² |
| Put the values | 250 = P × (5/100)² |
| Simplify | 250 = P × 1/400 |
| Sum | P = 250 × 400 = ₹1,00,000 |
Check: simple interest = 1,00,000 × 5% × 2 = 10,000.
Compound interest = 1,00,000 × 1.05 × 1.05 − 1,00,000 = 10,250.
Difference = 250.
Answer: (a) ₹1,00,000.
Why each option is right or wrong
- (a) CORRECT. P × (0.05)² = 250 gives P = ₹1,00,000.
- (b) Incorrect. ₹80,000 gives a difference of only ₹200.
- (c) Incorrect. ₹40,000 gives a difference of only ₹100.
- (d) Incorrect. ₹1,20,000 gives a difference of ₹300.
Key point
For 2 years: CI − SI = P(R/100)². For 3 years: CI − SI = P(R/100)²(3 + R/100). At 5% for 2 years the difference is 1/400 of the sum.
Remember
Two years: CI − SI = P × (R/100)².
Common mistakes
- Using the three-year formula for a two-year problem.
- Squaring 5 but forgetting to square the 100, giving P × 25/100.
- Taking the difference as 5% of the sum instead of 5% of the first year's interest.
Exam tip
Educated guess: at 5% the difference is 1/400 of the sum. So multiply 250 by 400. You can also test options: 1% of 1% of ₹1,00,000 is ₹10, and 25 times that is ₹250.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities (compound interest)
- R. S. Aggarwal, Quantitative Aptitude — Compound Interest