Question : A certain sum of money becomes triple itself in 26 years at simple interest. In how many years it will become five times of itself?
Option 1: 64 years
Option 2: 52 years
Option 3: 56 years
Option 4: 60 years
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Correct Answer: 52 years
Solution :
Given: Let the principal be $P$.
A sum of money becomes triple of itself in 26 years.
Simple interest in this case $=3P-P=2P$
Let the time taken for the amount $P$ to $5P$ be $x$ years.
Simple interest in this case: $5P-P= 4P$
We know simple interest on amount $P$ at $r$% rate of interest in $t$ years = $\frac{Prt}{100}$
For the same rate of interest $r$, Simple interest is directly proportional to the time $t$ years.
So, $\frac{2P}{4P}=\frac{26}{x}$
$⇒\frac{1}{2} = \frac{26}{x}$
$⇒x=52$ years
Hence, the correct answer is 52 years.
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