The difference between the simple interest received from two different sources on ₹ 1500 for 3 years is ₹ 13.50. The difference between their rates of interest is

### Concept & Difference in Rates The difference in simple interest accrued on the same principal over the same time period is directly proportional to the difference in their interest rates. Formula for difference in Simple Interest: $$\Delta SI = \frac{P \times \Delta R \times T}{100}$$ ### Step-by-Step Solution - **Given:** - Principal $P = 1500$ - Time $T = 3$ years - Difference in interest $\Delta SI = 13.50$ - Let the rates of interest be $R_1$ and $R_2$. The difference is $\Delta R = R_1 - R_2$. - **Calculation:** - Substitute the values into the formula: $13.50 = \frac{1500 \times \Delta R \times 3}{100}$ - Simplify the right side: $13.50 = 45 \times \Delta R$ - Solve for the difference in rates: $\Delta R = \frac{13.50}{45}$ - $\Delta R = 0.3\%$ ### Exam Strategy & Shortcut To find the difference in rates quickly, calculate the difference in interest for 1 year, which is $13.50 / 3 = 4.50$. The difference in rate is simply what percent this $4.50$ is of the principal $1500$. $\Delta R = \frac{4.50}{1500} \times 100 = 0.3\%$. ### Common Pitfall Avoid the trap of setting up two separate full equations and trying to solve for individual rates $R_1$ and $R_2$, which is impossible and wastes time. Only their difference can be found. ### Final Answer Therefore, the correct answer is **0.3%**.