Question

A sum of money becomes $\frac{7}{6}$ of itself in $3$ years at a certain rate of simple interest. In how many years will the sum become $3$ times of itself at the same rate.

• A. $9$ years
• B. $12$ years
• C. $20$ years
• D. $36$ years

Answer 1

The correct option is D $36$ years

Let the sum $=x$ Rs.

then amount $=\frac{7x}{6}$

Then S.I $=\frac{7x}{6}-x=\frac{x}{6}$

$S.I=\frac{P\times R\times T}{100}$

$R=\frac{S.I\times 100}{P\times T}$

$R=\frac{\frac{x}{6}\times 100}{x\times 3}=\frac{50}{9}$ $\%$

If amount $=$ Rs. $3x$, then S.I $=3x-x=2x$

$T=\frac{2x\times 100\times 9}{x\times 50}$

$T=2\times 2\times 9=36$ years.