The simple interest accrued on a certain principal in 5 years at the rate of 12 p.c.p.a. is ₹ 1536. What amount of simple interest would one get if one invests ₹ 1000 more than the previous principal for 2 years and at the same rate p.c.p.a.?

### Concept & Formula The relationship between Simple Interest (SI), Principal (P), Rate (R), and Time (T) is given by: $$SI = \frac{P \times R \times T}{100}$$ ### Step-by-Step Solution 1. **Given:** Initial $SI = 1536$, $T = 5$ years, $R = 12\%$ p.a. 2. Find the initial Principal ($P$): $1536 = \frac{P \times 12 \times 5}{100}$ 3. $1536 = P \times 0.6 \implies P = \frac{1536}{0.6} = 2560$ 4. **New Scenario:** The new Principal is $2560 + 1000 = 3560$. 5. The new Time ($T$) is $2$ years, and the Rate ($R$) is still $12\%$ p.a. 6. Calculate the new SI: $New SI = \frac{3560 \times 12 \times 2}{100} = \frac{3560 \times 24}{100} = 854.40$ 7. Since ₹ 854.40 is not among options (a) to (d), the answer is "None of these". ### Exam Strategy & Shortcut Instead of finding the total new SI all at once, you can calculate the SI on the original principal for 2 years ($\frac{2560 \times 12 \times 2}{100} = 614.40$) and add the SI on the extra ₹ 1000 ($\frac{1000 \times 12 \times 2}{100} = 240$). Then, $614.40 + 240 = 854.40$. ### Common Pitfall A common mistake is forgetting to add the ₹ 1000 to the original principal, which would lead to calculating the interest only on the initial principal (resulting in ₹ 614.40, option A). ### Final Answer Therefore, the correct answer is **None of these**.