A shopkeeper took a loan at 9% per annum simple interest for 2 years and repaid Rs 42952 in all, including interest. What was the amount of the loan?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 36400
The repayment is the loan plus the interest, so it equals the loan multiplied by \(\displaystyle 1+\frac{rt}{100}\).
Interest for 2 years \(=9\times2=18\%\) of the loan
Repayment \(=118\%\) of the loan \(=42952\)
Loan \(\displaystyle =\frac{42952\times100}{118}=36400\)
The loan was Rs 36400.
Why the other options are incorrect
Option (1) Rs 35200 — Incorrect. Interest on Rs 35200 for 2 years at 9% is Rs 6336, so the repayment would be Rs 41536, not Rs 42952.
Option (2) Rs 36000 — Incorrect. Interest on Rs 36000 for 2 years at 9% is Rs 6480, so the repayment would be Rs 42480, not Rs 42952.
Option (4) Rs 37800 — Incorrect. Interest on Rs 37800 for 2 years at 9% is Rs 6804, so the repayment would be Rs 44604, not Rs 42952.