The interest on a certain deposit at 4.5% p.a. is ₹ 202.50 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a. ?

### Concept & Formula Simple interest is directly proportional to the rate of interest when the principal and time are constant. $$SI \propto Rate$$ ### Step-by-Step Solution 1. **Given:** Interest at 4.5% = ₹ 202.50. 2. The question asks for the *additional* interest if the rate increases from 4.5% to 5%. 3. The increase in the interest rate is $5\% - 4.5\% = 0.5\%$. 4. Since 4.5% corresponds to ₹ 202.50, we can use the unitary method to find the value corresponding to 0.5%. 5. Value of 0.5% = $\frac{202.50}{4.5} \times 0.5$ 6. Simplify the fraction: $\frac{0.5}{4.5} = \frac{1}{9}$ 7. Additional interest = $\frac{1}{9} \times 202.50 = 22.50$ ### Exam Strategy & Shortcut Instead of calculating the principal, recognize that the extra interest is generated purely by the extra 0.5% rate. The ratio of the additional rate (0.5%) to the original rate (4.5%) is 1:9. Simply divide the original interest by 9 to get the answer instantly: $202.50 / 9 = 22.50$. ### Common Pitfall A common time-waster is calculating the full principal sum ($P = \frac{202.50 \times 100}{4.5 \times 1} = 4500$), then calculating the new total interest at 5% ($225$), and finally subtracting to find the difference ($225 - 202.50 = 22.50$). ### Final Answer Therefore, the correct answer is **₹ 22.50**.