Under simple interest, an amount becomes ₹812 in 2 years and ₹924 in 4 years. What is the annual rate of simple interest on the original principal?

Introduction:
This question tests how amounts grow under simple interest across different time periods. Under simple interest, the increase in amount per year is constant because interest added each year is the same. By comparing amounts at 2 years and 4 years, we can find the yearly interest, then compute principal and finally the rate.

Given Data / Assumptions:

• Amount after 2 years: A2 = ₹812
• Amount after 4 years: A4 = ₹924
• Simple interest implies constant yearly interest
• Amount relation: A = P + SI, with SI = (P * r * t) / 100

Concept / Approach:
Compute the difference A4 - A2 to find interest earned in the extra 2 years. Divide by 2 to get interest per year. Then subtract 2 years of interest from A2 to obtain the principal. Finally compute r using yearly interest = (P * r)/100.

Step-by-Step Solution:
Difference in amount from 2 to 4 years = 924 - 812 = 112 This 112 is interest for 2 years, so yearly interest = 112 / 2 = 56 At 2 years, total interest = 2 * 56 = 112 Principal P = A2 - interest in 2 years = 812 - 112 = 700 Yearly interest = (P * r) / 100, so 56 = (700 * r) / 100 r = (56 * 100) / 700 = 8

Verification / Alternative check:
Check using A4: interest in 4 years = 4 * 56 = 224, so A4 = 700 + 224 = 924, matching the given value.

Why Other Options Are Wrong:
7.2% yields yearly interest 50.4 on principal 700, which would not match the observed increase. 8.5% and 9.3% produce larger increases and would overshoot the amounts. 6.8% is too low.

Common Pitfalls:
Treating the growth as compound interest, or forgetting that the difference between amounts corresponds only to interest over the additional years under simple interest.

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