Simple Interest — A sum amounts to ₹ 1350 in 5 years and to ₹ 1620 in 8 years at the same simple interest rate. Find the principal (original sum).

Introduction / Context:
Two different future amounts at the same simple interest rate allow us to extract the yearly interest from their difference and then deduce the principal.

Given Data / Assumptions:

• A5 = ₹ 1350 at t = 5 years.
• A8 = ₹ 1620 at t = 8 years.
• Simple interest; principal remains constant.

Concept / Approach:
Difference between amounts over 3 years equals 3 years of interest: (A8 − A5) = 3 * I_per_year.

Step-by-Step Solution:
A8 − A5 = 1620 − 1350 = ₹ 270.Therefore I_per_year = 270 / 3 = ₹ 90.A5 = P + 5 * 90 = 1350 ⇒ P = 1350 − 450 = ₹ 900.

Verification / Alternative check:
Check A8: P + 8 * 90 = 900 + 720 = 1620, matches.

Why Other Options Are Wrong:
₹ 700, ₹ 800, ₹ 850, ₹ 1000 do not reproduce both amounts when forward-checked.

Common Pitfalls:
Using compounding or changing principal; SI keeps principal constant and adds equal yearly interest.

Final Answer:
₹ 900