Question

A reduction of $20\%$ in the price of sugar enables Mrs. Shah to buy an extra $3kg$ of it for $Rs.360$. Find

$\left(i\right)$ the original rate,
$\left(ii\right)$ the reduced rate per $kg$.

Answer 1

Given:

Let the original price of sugar be $Rs.x$

Reduced Rate per Kg $=(100-20)\%$ of $x$

$=80\%$ of $x$

$=\frac{80}{100}\times x$

$=\frac{4x}{5}$ per kg

Quantity of sugar for $Rs.360$ at the original rate $=\frac{360}{x}$

Quantity of Sugar for $Rs.360$ at the reduced rate $=\frac{360}{\frac{4x}{5}}$$=\frac{450}{x}$ kg

Difference in quantity $=3$

$\therefore \frac{450}{x}-\frac{360}{x}=3$

$\Rightarrow 450-360=3x$

$\Rightarrow x=Rs.30$

$\therefore$ Original price $=Rs.30$

Reduced price $=\frac{4x}{5}=\frac{4\times 30}{5}=Rs.24$