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).

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:

Verification / Alternative check:

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.