₹ 1000 is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become ₹ 2000 after

### Concept & Logic When simple interest is added to the principal at a fixed interval, it becomes a multi-stage simple interest problem where the principal changes for the subsequent periods. ### Step-by-Step Solution * **Given:** * Initial Principal ($P_1$) = ₹ 1000 * Rate ($R$) = 5% p.a. * Target Amount = ₹ 2000 * **Calculate Interest for first 10 years:** * $SI_1 = \frac{1000 \times 5 \times 10}{100} = 500$ * Amount after 10 years = $1000 + 500 = 1500$ * **Calculate remaining required interest:** * The new principal ($P_2$) for the next period is ₹ 1500. * We need the amount to reach ₹ 2000. * Required Interest = $2000 - 1500 = 500$ * **Calculate time for new principal to earn required interest:** * Let the additional time be $T$ years. * $500 = \frac{1500 \times 5 \times T}{100}$ * $500 = 75 \times T$ * $T = \frac{500}{75} = \frac{20}{3} = 6\frac{2}{3}$ years * **Calculate Total Time:** * Total Time = $10 \text{ years} + 6\frac{2}{3} \text{ years} = 16\frac{2}{3} \text{ years}$ ### Exam Strategy & Shortcut Observe the first 10 years yield ₹ 500 interest on ₹ 1000. Now you have ₹ 1500 and need ₹ 500 more. At 5%, ₹ 1500 generates ₹ 75 per year. $\frac{500}{75}$ simplifies instantly to $\frac{20}{3}$, or $6\frac{2}{3}$. Add this to the initial 10 years for $16\frac{2}{3}$. ### Common Pitfall Assuming simple interest remains constant across the entire period and solving for $2000 = 1000 + \frac{1000 \times 5 \times T}{100}$, which gives 20 years. This ignores the condition that interest is added to the principal after 10 years. ### Final Answer Therefore, the correct answer is **$16\frac{2}{3}$ years**.