In what time will Rs. 1,860 amount to Rs. 2,641.20 at 12% per annum simple interest?

Introduction / Context:
This question focuses on finding the time taken for a sum of money to grow to a given amount at a specified simple interest rate. Instead of directly giving the interest, the exam provides the final amount, so the first step is to find the interest and then use the simple interest formula to solve for time.

Given Data / Assumptions:

• Principal (P) = Rs. 1,860
• Final amount (A) = Rs. 2,641.20
• Rate (R) = 12% per annum
• Simple interest is applied

Concept / Approach:
First compute simple interest as the difference between amount and principal:
SI = A - PThen apply the formula for simple interest and rearrange to find time:
SI = (P * R * T) / 100T = (SI * 100) / (P * R)Careful arithmetic with decimals is important to reach the exact time value.

Step-by-Step Solution:
SI = A - P = 2641.20 - 1860 = Rs. 781.20Now use SI formula: 781.20 = (1860 * 12 * T) / 100Compute denominator: (1860 * 12) / 100 = 1860 * 0.12 = 223.20So 781.20 = 223.20 * TT = 781.20 / 223.20T = 3.5 years
Verification / Alternative check:
Check by forward calculation. Interest per year at 12% is:
Yearly interest = (1860 * 12) / 100 = Rs. 223.20In 3.5 years, total interest = 223.20 * 3.5 = 781.20Final amount = principal + interest = 1860 + 781.20 = 2641.20This matches the given amount, confirming that 3.5 years is correct.

Why Other Options Are Wrong:
For 2.9 years, interest would be significantly less than 781.20, giving a lower final amount. For 4.2 or 4.7 years, the interest would exceed 781.20 and the final amount would be higher than Rs. 2,641.20. Only 3.5 years gives an exact match.

Common Pitfalls:
Errors often arise from incorrectly subtracting the principal from the amount or mishandling the decimal arithmetic when dividing 781.20 by 223.20. Also, some students forget to divide by 100 in the simple interest formula. Writing each step clearly helps avoid these issues.

Final Answer:
The required time is 3.5 years.