Question

If the price of the wheat is increased by 30%. Then by what % should a family decrease the consumption of wheat, so that there is no change in the expenditure.

Answer 1

Let ${}^{\prime }{x}^{\prime }$ be cost of wheat and ${}^{\prime }{y}^{\prime }$ be household consumption.

$\therefore$ Initial expense $=xy$

Let new consumption $=a$

new cost $=x(1+\frac{30}{100})$

$=\frac{13x}{10}$

To keep expenditure same,

new expense $=$ old (initial) expense.

$\Rightarrow \frac{13x}{10}\times a=xy$

$\Rightarrow a=\frac{10}{13}y$

decrease in consumption $=y-a$

$=y-\frac{10}{13}y$

$=\frac{3}{13}y$

$\therefore$ % decrease $=\frac{\frac{3y}{13}}{y}\times 100$%

$=\frac{3}{13}\times 100$

$=23.076$%