Simple Interest — Compare two scenarios to find principal: SI on a sum for 2 1/2 years at 12% p.a. is ₹ 20 less than the SI on the same sum for 3 1/2 years at 10% p.a. Find the sum.

Introduction / Context:
Comparative SI statements produce a single linear equation in the principal when time and rate differ. Careful reading of “less than” ensures the equation’s direction is correct.

Given Data / Assumptions:

• SI1 (2.5 years at 12%) is ₹ 20 less than SI2 (3.5 years at 10%).
• Let principal be P.

Concept / Approach:
Write P * 0.12 * 2.5 + 20 = P * 0.10 * 3.5 and solve for P. All quantities are linear in P under SI.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Other values of P fail to keep a consistent ₹ 20 gap between the two computed SIs.

Common Pitfalls:

• Reversing “less than” and writing 0.30 P = 0.35 P + 20, which yields a negative P.

Final Answer:
₹ 400.