Simple Interest — Equal principals, different durations: Two equal sums are deposited at 15% per annum, one for 3.5 years and the other for 5 years. If the difference between the interests earned is ₹ 144, find each principal amount.

Introduction / Context:
This problem uses the linearity of simple interest with respect to both time and principal. The same rate applies to the same principal, but for different durations—so the interest difference isolates the time difference effect.

Given Data / Assumptions:

• Rate r = 15% per annum
• Times t1 = 3.5 years, t2 = 5 years
• Difference in interest ΔI = ₹ 144
• Equal principals = P (each)

Concept / Approach:
Simple interest I = (P * r * t) / 100. Hence ΔI = P * r * (t2 - t1) / 100. Solve for P using the known gap in time and rate.

Step-by-Step Solution:
Δt = 5 - 3.5 = 1.5 yearsΔI = P * 15 * 1.5 / 100 = 0.225 * P144 = 0.225 * PP = 144 / 0.225 = ₹ 640

Verification / Alternative check:
Interest for 5 years: 640 * 15 * 5 / 100 = 640 * 0.75 = ₹ 480. For 3.5 years: 640 * 15 * 3.5 / 100 = 640 * 0.525 = ₹ 336. Difference = ₹ 144 (correct).

Why Other Options Are Wrong:
₹ 460, ₹ 500, ₹ 560, and ₹ 720 do not produce the required 144 difference when substituted into the SI expression with the given times.

Common Pitfalls:
Using the amount difference instead of interest difference, or forgetting to divide by 100 when applying the SI formula.

Final Answer:
₹ 640