A sum becomes ₹1,392 in 2 years and ₹1,488 in 3 years at simple interest. What is the annual rate of simple interest (in % per annum)?

Introduction:
This question tests the defining property of simple interest: the amount increases by the same interest each year. When you are given amounts at two different times, the difference between those amounts represents interest earned during the extra time period. From that, you can find the yearly interest, the principal, and then the rate. This is a standard “two amounts at two times” simple interest pattern.

Given Data / Assumptions:

• Amount after 2 years: A2 = ₹1,392
• Amount after 3 years: A3 = ₹1,488
• Under simple interest, yearly interest is constant
• Formula: A = P + SI and SI = (P * r * t) / 100

Concept / Approach:
Compute the difference A3 - A2 to get interest earned in 1 extra year. That difference equals the yearly interest. Then subtract 2 years of yearly interest from A2 to get the principal P. Finally compute r using yearly interest = (P * r) / 100.

Step-by-Step Solution:
Interest for the 3rd year = A3 - A2 = 1488 - 1392 = 96 So yearly interest = 96 Interest in 2 years = 2 * 96 = 192 Principal P = A2 - 192 = 1392 - 192 = 1200 Yearly interest = (P * r) / 100 96 = (1200 * r) / 100 r = (96 * 100) / 1200 = 8

Verification / Alternative check:
At 8% on ₹1200, yearly interest is ₹96. Amount after 2 years = 1200 + 192 = 1392, and after 3 years = 1200 + 288 = 1488, both matching the given values.

Why Other Options Are Wrong:
10% would make yearly interest 120 on a principal near 1200, causing a larger yearly increase than 96. 12% is even larger. 8.5% gives a non-matching yearly difference. 6% is too low to reach the given amounts.

Common Pitfalls:
Treating the amounts as compound growth, or forgetting that the difference between A3 and A2 is exactly one year of interest under simple interest.

Final Answer:
The annual simple interest rate is 8% per annum.