CI vs SI on Same Sum and Rate — Recover principal from 2-year totals: The simple interest on a certain sum for 2 years is ₹ 40, while the compound interest on the same sum for the same rate and 2 years is ₹ 45. Find the principal.
Aptitude
Compound Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: Rs. 80
Explanation
Introduction / Context:For two years at the same annual rate r (decimal), SI(2y) = 2 P r, and CI(2y) = 2 P r + P r^2. The difference isolates the interest-on-interest term P r^2, letting us solve for r and/or P using the two totals provided.
Given Data / Assumptions:
- SI over 2 years = ₹ 40 ⇒ 2 P r = 40
- CI over 2 years = ₹ 45 ⇒ 2 P r + P r^2 = 45
- Same sum and same rate for both measures
Concept / Approach:Subtract to get P r^2 = 5. From 2 P r = 40 infer P r = 20. Then r = (P r^2)/(P r) = 5 / 20 = 0.25 (25%). Finally, compute P = (P r)/r = 20 / 0.25 = 80.
Step-by-Step Solution:
P r = 20; P r^2 = 5; r = 0.25.Principal P = 20 / 0.25 = ₹ 80.Check: SI = 2 * 80 * 0.25 = ₹ 40; CI = SI + P r^2 = 40 + 5 = ₹ 45.Verification / Alternative check:
Forward compute amounts to confirm interest breakdowns match the totals.Why Other Options Are Wrong:
- ₹ 70, ₹ 85, ₹ 90, ₹ 75 do not simultaneously satisfy SI = 40 and CI = 45 at one common rate.
Common Pitfalls:
- Mistaking the 5 difference as the rate itself; it represents P r^2, not r.
Final Answer:Rs. 80.