Question : A certain sum of money becomes triple itself in 8 years at simple interest. In how many years it will become five times of itself?
Option 1: 16 years
Option 2: 7 years
Option 3: 10 years
Option 4: 12 years
Correct Answer: 16 years
Solution :
Given: A certain sum of money becomes triple itself in 8 years at simple interest.
Let $P$ be the principal, the interest rate be $R$ and simple interest be $2P$ after 8 years.
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
⇒ $2P=\frac{P\times R\times 8}{100}$
⇒ $R=\frac{2P\times 100}{P\times 8}=25\%$
Now, the principal becomes $5P$, then the interest would be $4P$ in $T$ years and the rate of interest is 25%.
⇒ $4P=\frac{P\times T\times 25}{100}$
⇒ $T=\frac{4P\times 100}{P\times 25}=16$ years
Hence, the correct answer is 16 years.
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