For how many years must a sum of Rs. 1,250 be invested at 12.5% per annum simple interest so that it grows to Rs. 10,000?

Introduction / Context:
This question involves finding the time required for a sum to grow from its original value to a much larger final amount at simple interest. The data show that the amount increases eight times from 1,250 to 10,000, so the total interest is large. The problem tests the ability to find time when principal, rate, and final amount are given.

Given Data / Assumptions:

• Principal (P) = Rs. 1,250
• Final amount (A) = Rs. 10,000
• Rate (R) = 12.5% per annum
• Simple interest is applied
• We must find time (T) in years

Concept / Approach:
First find the simple interest by subtracting the principal from the final amount. Then apply the simple interest formula rearranged to solve for time:
SI = A - PSI = (P * R * T) / 100T = (SI * 100) / (P * R)Careful handling of the decimal rate 12.5% is also important; it is convenient to treat it as 1 / 8.

Step-by-Step Solution:
SI = A - P = 10000 - 1250 = Rs. 8,750Now use SI formula: 8750 = (1250 * 12.5 * T) / 10012.5 = 1 / 8, so 1250 * 12.5 = 1250 * (1 / 8) * 100 = 15625, but a direct numeric approach is also fineCompute denominator: (1250 * 12.5) / 100 = 1250 * 0.125 = 156.25So 8750 = 156.25 * TT = 8750 / 156.25T = 56 years
Verification / Alternative check:
Check reasonableness. At 12.5% per year, interest each year on Rs. 1,250 is 1250 * 12.5 / 100 = Rs. 156.25. Over 56 years, interest earned is 156.25 * 56 = 8,750. Adding this to the principal gives 1,250 + 8,750 = 10,000, which matches the target amount exactly.

Why Other Options Are Wrong:
For 45 years, interest would be 156.25 * 45 = 7,031.25, giving an amount less than 10,000. For 57 or 65 years, interest would be greater than 8,750, giving a final amount larger than 10,000. Thus, only 56 years gives the correct final amount.

Common Pitfalls:
Some candidates mis-handle the rate 12.5% and treat it as 12% or 12.05%. Others forget to subtract the principal from the final amount to get the actual interest before applying the formula. Because the time value is large, small calculation mistakes can lead to obviously unreasonable answers, so it is useful to perform a quick sanity check at the end.

Final Answer:
The required time is 56 years.