Question

The price of a commodity is increased by 40% . By what percent shuld a consumer reduce his consumption so that his expenditure on the commodity remains constant ?

Answer 1

Let the initial consumption be $x$ and price of commodity be $100$.

Expenditure$=100x$

When commodity increased by $40\%$.

Price of commodity $140\%\times 100=140$.

Then the consumption be $y$.

Expenditure$=140y$

Given,$100x=140y⟹\frac{y}{x}=\frac{100}{140}$

$\%$ reduce in consumption$=\frac{x-y}{x}\times 100$

$⟹\frac{140-100}{140}\times 100=28.57\%$.