A person borrows ₹ 75,000 for 3 years at 5% simple interest. He lends it to B at 7% for 3 years. What is his gain (in ₹)?

Appeared in: PGIMER Chandigarh NO - 2015

Explanation

The problem involves calculating the net gain from a financial transaction where money is borrowed at a lower simple interest rate and lent out at a higher simple interest rate.
The gain is the difference between the interest earned and the interest paid over the same principal amount and time period.
The effective annual gain in interest rate is the difference between the lending rate (7%) and the borrowing rate (5%), which is 2%.
To find the total gain, this net rate is applied to the principal for the given time period using the simple interest formula.
Calculation: Gain = (Principal × Net Rate × Time) / 100 = (₹75,000 × 2 × 3) / 100 = ₹4,500.

Option A: This value is incorrect. It may result from a calculation error, such as miscalculating the net interest rate or the total time.
Option C: This amount is incorrect. It would be the gain if the time period was different.
Option D: This value is incorrect and likely the result of a calculation error or rounding.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating profit from borrowing and lending on simple interest as background academic context rather than a clinical decision trigger.
Understanding simple interest is a fundamental financial literacy skill, important for managing personal loans, savings, and investments.
The concept of an interest rate differential (or 'spread') is the basic principle by which banks and financial institutions generate profit.
This type of calculation helps in making informed decisions when considering taking a loan for investment purposes.

How to Approach the Question

First, identify the key variables given in the problem: Principal (P), Time (T), Borrowing Rate (R1), and Lending Rate (R2).
Recognize that the 'gain' is the difference between the total interest received and the total interest paid.
The most efficient method is to calculate the net interest rate per year, which is the difference between the lending rate and the borrowing rate (R2 - R1).
Apply the simple interest formula (SI = P × R × T / 100) using the net interest rate to find the total gain over the entire period.
Alternatively, calculate the interest paid and interest received separately, then subtract the former from the latter to find the gain.
Finally, double-check your calculation and match the result with the given options.

Concept Tested & Keywords

Concept Tested: Calculating profit from borrowing and lending on simple interest.
Stem keywords: borrows, lends, simple interest, gain, ₹ 75,000, 3 years, 5%, 7%
Lead-in keywords: What is his gain

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Attempt every question from this paper in a timed mock, then review the full solution for each one.