Question

A sum of money at C.I amounts to thrice itself in $6$ years.Find in how many years will it be $9$ times itself

• A. $5$
• B. $6$
• C. $7$
• D. $12$

Answer 1

Answer: (D)

$12$

Let the principle be $x$.

According to the question,

$3x=x{(1+\frac{R}{100})}^6$

$3={(1+\frac{R}{100})}^6$ $..........\left(1\right)$

Now,

Let it is $9$ times in $T$ years, then

$9x=x{(1+\frac{R}{100})}^T$

$3^2={(1+\frac{R}{100})}^T$

From equation $\left(1\right)$, we get

${\left({(1+\frac{R}{100})}^2\right)}^6={(1+\frac{R}{100})}^T$

${(1+\frac{R}{100})}^{12}={(1+\frac{R}{100})}^T$

On comparing both sides, we get

$T=12years$

Hence, this is the answer.