A person borrows ₹ 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at $6\frac{1}{4}\%$ p.a. for 2 years. Find his gain in the transaction per year.

### Concept & Logic The net gain per year when borrowing at one rate and immediately lending at a higher rate is simply the difference between the two interest rates applied to the principal. $$Gain = \frac{P \times (R_2 - R_1) \times T}{100}$$ ### Step-by-Step Solution * **Given:** * Principal ($P$) = ₹ 5000 * Borrowing Rate ($R_1$) = 4% p.a. * Lending Rate ($R_2$) = $6\frac{1}{4}\% = 6.25\%$ p.a. * **Calculate net rate difference per year:** * Net Rate = $6.25\% - 4\% = 2.25\%$ * **Calculate gain per year:** * Note that the question asks for gain *per year*, so $T = 1$. * $Gain = \frac{5000 \times 2.25 \times 1}{100}$ * $Gain = 50 \times 2.25 = 112.50$ ### Exam Strategy & Shortcut You only need to compute the interest difference for one year. The difference in rates is $2.25\%$. $1\%$ of 5000 is 50. So, $2.25 \times 50 = 112.50$. This avoids calculating the full 2-year interest and subtracting, which wastes valuable time. ### Common Pitfall Many students calculate the total gain over the 2-year period and forget to divide by 2 at the end, answering with ₹ 225 instead of the gain *per year*. ### Final Answer Therefore, the correct answer is **₹ 112.50**.