Introduction / Context:This question tests the basic concept of simple interest and how a person can earn a profit by borrowing money at a lower rate and lending it at a higher rate. The key idea is that the difference between the two interests over the same principal and time period becomes the person's gain. We are asked to find the gain per year in rupees.Given Data / Assumptions:
- Principal borrowed = Rs. 5,000
- Time period = 2 years
- Rate of interest paid = 4% per annum (simple interest)
- Rate of interest charged = 6.25% per annum (simple interest)
- Same principal and same time period for both transactions
Concept / Approach:The formula for simple interest is:
Simple interest = (Principal * Rate * Time) / 100We first compute the interest the person pays at 4% and then the interest he receives at 6.25%. The difference between these two amounts over 2 years is his total gain. Dividing this gain by the time period gives the gain per year.
Step-by-Step Solution:Interest paid at 4% for 2 years = (5000 * 4 * 2) / 100 = 5000 * 0.08 = Rs. 400Interest received at 6.25% for 2 years = (5000 * 6.25 * 2) / 100 = 5000 * 0.125 = Rs. 625Total gain over 2 years = Interest received - Interest paid = 625 - 400 = Rs. 225Gain per year = Total gain / Time = 225 / 2 = Rs. 112.50Verification / Alternative check:We can think in terms of effective net rate. The net extra rate the person earns is 6.25% - 4% = 2.25% per annum on Rs. 5,000. So gain per year should be:
Net gain per year = (5000 * 2.25 * 1) / 100 = 5000 * 0.0225 = Rs. 112.50This matches the previous calculation, confirming that the answer is consistent.
Why Other Options Are Wrong:Rs. 150.25, Rs. 167.50 and Rs. 170 correspond to larger gains that would require either a higher difference in interest rates or a longer time period. They do not match the simple interest calculations using the given data.
Common Pitfalls:Students sometimes compute the total gain correctly but forget to divide by the number of years, thus giving the gain for 2 years instead of the gain per year. Another common error is to apply the higher rate to the difference of the rates instead of to the principal.
Final Answer:The gain in the transaction per year is
Rs. 112.50.
