MCQ
Mark $(\checkmark)$ against the correct answer in the following: At simple interest a sum becomes $\frac65$ of itself in $2\frac12$ years. The rate of interest per annum is:
- A$6\%$
- B$7\frac12\%$
- ✓$8\%$
- D$9\%$
Let the sum be $Rs. x$
Rate of interest $= r%$
Time $=2\frac12$ years $=\frac52$ years
Amount $=\frac65\times\text{Sum}$
Rate $= ?$
Amount $=\frac65\times\text{Sum}$
Principal $+ S.I. =$ Amount
$\text{Principal}+\frac{\text{Principal}\times\text{Rate}\times\text{Time}}{100}=\frac65\times\text{Principal}$
$\Rightarrow\text{x}+\frac{\text{x}\times\text{r}\times5}{100\times2}=\frac65\text{x}$
$\Rightarrow\text{x}\Big(1+\frac{5\text{r}}{100\times2}\Big)=\frac65\text{x}$
$\Rightarrow1+\frac{\text{r}}{40}=\frac65$
$\Rightarrow\text{r}=40\times\frac15$
$\Rightarrow\text{r}=8$
So, the rate of interest is $8\%$
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