Question

A sum of money, lent out at simple interest, doubles itself in $8$ years. Find in how many years will the sum become triple (three times) of itself at the same rate per cent ?

• A. $11$ years
• B. $13$ years
• C. $14$ years
• D. $16$ years

Answer 1

The correct option is D $16$ years

Simple Interest $I=\frac{PNR}{100}$
Amount $A=2P$
$I=A-P=2P-P=P$
$N=8$ years

So, $P=\frac{P\times 8\times R}{100}$
$\Rightarrow R=12.5$ %

Now, we need to find $N$ when $A=3P$
$\Rightarrow I=3P-P=2P$
So, $2P=\frac{P\times N\times 12.5}{100}$
$\Rightarrow N=16$ years