Question

$\text{In what time will the interest on a certain}\text{sum at 7.5\% simple interest be}\frac{3}{4}\text{times of itself?}$

• A. 12 years
• B. 8 years
• C. 10 years
• D. 14 years

Answer 1

The correct option is C

10 years

$\text{Let the principal (P) be}x.$

$\text{Rate of interest, R = 7.5\%}$

$\text{Let the time period be T.}$

$\text{According to the question, interest is}\frac{3}{4}\text{times the principal.}$

$\text{Simple interest, S.I. =}\frac{3}{4}x$

We know that simple interest,

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

$\Rightarrow \frac{3x}{4}=\frac{x\times 7.5\times T}{100}$

$\Rightarrow T=\frac{3\times 100}{7.5\times 4}$

$\Rightarrow T=10\text{years}$