A certain sum of money lent at simple interest for a certain time amounts to Rs 1620 at 7% per annum and to Rs 1440 at 4% per annum. Find the time.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5 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 \(P\).
\(\displaystyle\frac{P\times3\times t}{100}=1620-1440=180\), so \(P\times t=6000\)
At 4%: interest \(\displaystyle =\frac{4\times P t}{100}=\frac{4\times6000}{100}=240\)
\(P=1440-240=1200\)
\(t=6000\div1200=5\) years
The time is 5 years.
Why the other options are incorrect
Option (1) 4 years — Incorrect. With 4 years, the extra 3% would give \(P=1500\); then the amount at 4% would be Rs 1740, not Rs 1440.
Option (2) 6 years — Incorrect. With 6 years, the extra 3% would give \(P=1000\); then the amount at 4% would be Rs 1240, not Rs 1440.
Option (4) 8 years — Incorrect. With 8 years, the extra 3% would give \(P=750\); then the amount at 4% would be Rs 990, not Rs 1440.