Simple Interest – Recover the principal from two amounts: A certain sum amounts to Rs 1,040 in 3 years and Rs 1,360 in 7 years at simple interest. Find the principal (original sum).
Aptitude
Simple Interest
Difficulty: Medium
Choose an option
Answer
Correct Answer: Rs 800
Explanation
Introduction / Context:With SI, the difference in amounts over two times equals the uniform interest accrued during the gap. This reveals annual SI and then the principal.
Given Data / Assumptions:
- A3 = Rs 1040
- A7 = Rs 1360
Concept / Approach:Annual SI = (A7 - A3) / (7 - 3). Then P = A3 - 3 * (annual SI).
Step-by-Step Solution:
Annual SI = (1360 - 1040) / 4 = 320 / 4 = Rs 80Principal P = 1040 - 3 * 80 = 1040 - 240 = Rs 800Verification / Alternative check:
Check A7 = 800 + 7 * 80 = 1360 (matches)Why Other Options Are Wrong:
- Rs 750 / 900 / 1000 / 850: do not satisfy both given amounts under a single annual SI.
Common Pitfalls:
- Miscalculating the time gap (7 - 3).
Final Answer:Rs 800.