Simple Interest — ₹ 12,000 is placed at 10% p.a. simple interest. Because the depositor withdraws after 3 years (instead of keeping it for 5 years at 10%), the bank pays a lower simple-interest rate for the 3-year period. If his interest is ₹ 3,320 less than what he would have received at 5 years and 10%, find the rate actually allowed for the 3 years.

Introduction / Context:
Under simple interest, interest is proportional to time and rate. The question contrasts the interest that would have been earned over 5 years at 10% with the interest actually paid for 3 years at an unknown lower rate. The difference between these totals is known, allowing us to solve for the unknown rate.

Given Data / Assumptions:

• Principal P = ₹ 12,000.
• Benchmark (5 years at 10% SI): I_5y = P * 0.10 * 5 = ₹ 6,000.
• Actual (3 years at rate r SI): I_3y = P * r * 3.
• Shortfall relative to benchmark: I_5y − I_3y = ₹ 3,320.

Concept / Approach:
Set up the equation 12,000 * 0.10 * 5 − 12,000 * r * 3 = 3,320 and solve for r as a percentage.

Step-by-Step Solution:
6,000 − 36,000 r = 3,320.36,000 r = 6,000 − 3,320 = 2,680.r = 2,680 / 36,000 = 0.074444… = 7.444…% = 67/9%.

Verification / Alternative check:
Check: I_3y = 12,000 * 0.074444… * 3 = 2,680; shortfall = 6,000 − 2,680 = 3,320 (as given).

Why Other Options Are Wrong:
78/9%, 77/9%, 87/9% are around 8.6–9.7% and do not satisfy the shortfall equation; 7.25% also fails the equality.

Common Pitfalls:
Interpreting “less than” backward; ensure the equation subtracts actual from benchmark, not vice versa.

Final Answer:
67/9%