Simple Interest — A principal amounts to ₹ 944 in 3 years and ₹ 1040 in 5 years at the same simple interest rate. Find the principal.

Introduction / Context:Two amounts at different times under the same simple interest rate differ by a multiple of the annual interest. That difference allows quick extraction of the yearly interest and hence the principal.

Given Data / Assumptions:

• A3 = ₹ 944 at 3 years.
• A5 = ₹ 1040 at 5 years.

Concept / Approach:A5 − A3 = 2 years of interest. Let I be annual interest; then 2I = 1040 − 944 = 96 ⇒ I = 48. Now use A3 = P + 3I to get P.

Step-by-Step Solution:I = 48 per year.P = 944 − 3*48 = 944 − 144 = ₹ 800.

Verification / Alternative check:At 5 years: 800 + 5*48 = 1040, matches.

Why Other Options Are Wrong:Other choices fail the forward check against both 3-year and 5-year amounts.

Common Pitfalls:Mixing SI with compounding; only linear increments apply here.

Final Answer:₹ 800