₹750 is invested for 3 months and earns simple interest of ₹18. What is the annual rate of simple interest per annum (in %)?

Introduction:
This question tests finding an annual simple interest rate when time is given in months. The simple interest formula SI = (P * r * t) / 100 expects time in years when r is per annum. So we first convert 3 months into years, then solve for r. This involves one conversion plus a formula rearrangement, so it is medium difficulty.

Given Data / Assumptions:

• Principal P = ₹750
• Simple interest SI = ₹18
• Time = 3 months = 3/12 years = 0.25 years
• Rate r = ? % per annum
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Convert time to years because the rate is annual. Then rearrange r = (SI * 100) / (P * t). Substitute values carefully, keeping r as a percentage (not a decimal) since the formula divides by 100.

Step-by-Step Solution:
t = 3/12 = 0.25 years SI = (P * r * t) / 100 r = (SI * 100) / (P * t) r = (18 * 100) / (750 * 0.25) Denominator: 750 * 0.25 = 187.5 r = 1800 / 187.5 = 9.6

Verification / Alternative check:
At 9.6% per annum on ₹750, yearly interest is ₹72. In 3 months (1/4 year), interest is 72/4 = ₹18, matching the given interest.

Why Other Options Are Wrong:
12% would give yearly interest 90 and quarterly interest 22.5. 7.2% gives quarterly interest 13.5. 2.4% and 8% are also too low to produce ₹18 in 3 months on ₹750.

Common Pitfalls:
Forgetting to convert months to years, using t = 3 instead of 0.25, or treating 9.6% as 0.096 while still dividing by 100 again.

Final Answer:
The annual simple interest rate is 9.6% per annum.