A certain sum of money invested for a certain time at simple interest amounts to Rs 350 at 5% per annum, and to Rs 250 at 3% per annum. Find the time.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 50 years
The sum and the time are the same in both cases, so the difference of the two amounts is the interest at the difference of the rates.
Difference of the amounts \(=350-250=\) Rs 100, the interest at \(5\%-3\%=2\%\) per annum
So the interest at 1% per annum \(=\) Rs 50, and at 5% per annum \(=5\times50=\) Rs 250
Sum \(=\) amount at 5% \(-\) interest at 5% \(=350-250=\) Rs 100
Interest at 5%: \(\displaystyle \frac{100\times5\times T}{100}=250\), so \(5T=250\)
\(T=50\) years
Check at 3%: interest \(\displaystyle =\frac{100\times3\times50}{100}=150\), amount \(=100+150=\) Rs 250
The time is 50 years.