Manju borrows Rs. 5,000 for 2 years at 4% per annum simple interest from Sudha. She immediately lends the same amount to another person at 6.25% per annum simple interest for 2 years. What is her gain in this transaction per year?

Introduction / Context:
This problem is similar in structure to earlier simple interest gain questions. Manju acts as an intermediary, borrowing money at a lower rate and lending it out at a higher rate. The difference in interests over the same principal and time period becomes her profit. We are required to find her profit per year.

Given Data / Assumptions:

• Principal borrowed and lent = Rs. 5,000
• Time = 2 years
• Rate paid by Manju = 4% per annum simple interest
• Rate charged by Manju = 6.25% per annum simple interest
• We must find Manju's gain per year

Concept / Approach:
The formula for simple interest is:
SI = (P * R * T) / 100We calculate the interest Manju pays to Sudha at 4%, the interest she receives at 6.25%, and then take the difference, which is her total gain over 2 years. Dividing this by 2 gives the gain per year.

Step-by-Step Solution:
Interest paid to Sudha at 4% for 2 years:SI1 = (5000 * 4 * 2) / 100 = 5000 * 0.08 = Rs. 400Interest received from the other person at 6.25% for 2 years:SI2 = (5000 * 6.25 * 2) / 100 = 5000 * 0.125 = Rs. 625Total gain over 2 years = SI2 - SI1 = 625 - 400 = Rs. 225Gain per year = 225 / 2 = Rs. 112.50
Verification / Alternative check:
We can interpret the profit as arising from the net extra rate of interest. Net rate advantage = 6.25% - 4% = 2.25% per annum. Gain per year is therefore:
(5000 * 2.25) / 100 = 5000 * 0.0225 = Rs. 112.50This matches our earlier calculation, confirming consistency.

Why Other Options Are Wrong:
Values like Rs. 101, Rs. 98.5 or Rs. 124.3 do not correspond to the correct difference between the two simple interest amounts. They either understate or overstate the net gain that would arise from the given rate difference on Rs. 5,000 over 2 years.

Common Pitfalls:
Students may forget to divide the total gain for 2 years by 2, thereby giving the gain over the whole period instead of per year. Another mistake is to average the two rates instead of subtracting them to find the net advantage. Always remember that profit here is driven by the difference in interest rates applied to the same principal and time.

Final Answer:
Manju's gain in the transaction per year is Rs. 112.50.