A certain sum of money lent at simple interest for a certain time amounts to Rs 660 at 8% per annum and to Rs 600 at 5% per annum. Find the time.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4 years
The sum and the time are the same, so the difference of the amounts is the interest at the extra 3%; this gives \(P\times t\), and either amount then gives \(P\).
\(\displaystyle\frac{P\times3\times t}{100}=660-600=60\), so \(P\times t=2000\)
At 5%: interest \(\displaystyle =\frac{5\times P t}{100}=\frac{5\times2000}{100}=100\)
\(P=600-100=500\)
\(t=2000\div500=4\) years
The time is 4 years.
Why the other options are incorrect
Option (2) 8 years — Incorrect. With 8 years, the extra 3% would give \(P=250\); then the amount at 5% would be Rs 350, not Rs 600.
Option (3) 5 years — Incorrect. With 5 years, the extra 3% would give \(P=400\); then the amount at 5% would be Rs 500, not Rs 600.
Option (4) 2 years — Incorrect. With 2 years, the extra 3% would give \(P=1000\); then the amount at 5% would be Rs 1100, not Rs 600.