Question

Rajesh deposits a certain amount in a bank which becomes three times of itself in $16$ years. Find the time required by the same amount to become four times of itself.

Answer 1

Let $P$ be the principal amount, $r$ be the rate of interest.

Given:-

Amount $\left(A\right)=3P$

Time period $\left(t\right)=16\text{years}$

Therefore,

Simple interest $=3P-P=2P$

Now,

As we know that,

$S.I.=\frac{P\times r\times t}{100}.....\left(1\right)$

Here,

$S.I.=$ Simple interest

$P=$ Principal amount

$r=$ Rate

$t=$ Time period

$\therefore 2P=\frac{P\times r\times 16}{100}$

$\Rightarrow r=\frac{200}{16}=12.5\%$

Now let the amount becomes its $4$ times in times $t$ years.

Now,

$S.I.=4P-P=3P$

Therefore, from ${eq}^n\left(1\right)$, we have

$3P=\frac{P\times 12.5\times t}{100}$

$\Rightarrow t=\frac{300}{12.5}=24\text{years}$

Hence the time required by the amount to become its $4$ times is $24$ years.

Hence the correct answer is $24$ years.