A sum of money becomes $\frac{41}{40}$  of itself  in $\frac{1}{4}$  year at a certain rate of interest. The rate of interest per annum is

Time$T=\frac{1}{4}\text{years}$

Rate of interest $R=r\%p.a$

Total amount $=\text{Rs}\text{.}\frac{41}{40}x$

$\therefore$ Interest $=\text{Total}\text{amount}-\text{Principle}$

$=\frac{41}{40}x-x$

$=\frac{41x-40x}{40}=\frac{x}{40}$

But simple interest$I=\frac{PTR}{100}$

$\frac{x}{40}=\frac{x\times \frac{1}{4}\times r}{100}$

$\frac{1}{40}=\frac{r}{400}$

$\therefore r=10\%$