Question

At what rate percent per annum will the simple interest on a sum of money be $\frac{2}{5}$ of the amount in $10$ yrs.

• A. $4\%$
• B. $\frac{17}{3}\%$
• C. $6\%$
• D. $\frac{20}{3}\%$

Answer 1

The correct option is D $\frac{20}{3}\%$

Let the principal be $x$ , time $=10$ years , Rate$=r\%$ per annum

$\Rightarrow \frac{x\times r\times \times 10}{100}=\frac{2}{5}x+\frac{x\times r\times 10}{100}$

$\Rightarrow \frac{xr}{10}=\frac{2x}{5}+\frac{2xr}{50}$

$\Rightarrow \frac{xr}{10}-\frac{2xr}{50}=\frac{2x}{5}$

$\Rightarrow r=\frac{2\times 10}{3}=\frac{20}{3}$ $\%$