Question

The true discount on a bill is $\text{Rs.}1800$ and banker's discount is $\text{Rs.}1887$. If the bill is due $10$ months hence, find the rate of interest.

Answer 1

True discount $(T.D.)=Rs.1800$

Banker's discount $=Rs.1887$

Time period $\left(n\right)=10\text{months}=\frac{10}{12}=\frac{5}{6}\text{years}$

As we know that,

$\text{Banker's discount}=T.D.+\text{Interest on true discount}$

$⟹\text{Banker's discount}=1800+\frac{1800\times R\times 5}{6\times 100}$ $[\because \text{Simple interest}=\frac{P\times R\times T}{100}]$

$⟹1887=1800+15R$

$⟹87=15R$

$\Rightarrow R=\frac{87}{15}=\frac{29}{5}\%=5.8\%$

Hence the rate of interest is $5.8\%$.