• # question_answer The price of a commodity is increased by 40%. By what per cent should a consumer reduce his consumption so that his expenditure on the commodity remains constant? A)  $25\frac{4}{7}%$                   B)  $26\frac{4}{7}%$C)  $27\frac{4}{7}%$                   D)  $28\frac{4}{7}%$

(d): Let him consume 'x' kg previously Previous price = C Rs/kg $\Rightarrow \text{cost}=xC$ New price = 1.4C Rs/kg. Let new consumption decrease by p%. $\Rightarrow New\text{ }consumption=\frac{x(100-p)}{100}kg$ $\therefore New\,cost=\frac{x\left( 100-p \right)}{100}\times \left( 1.4C \right)$ $\therefore \frac{x\left( 100-p \right)}{100}\times \left( 1.4C \right)=xC$ $\Rightarrow 1.4(100-p)=100$ $\Rightarrow 140-1.4=100$ $\Rightarrow 40=1.4p$ $\Rightarrow p=\frac{40}{1.4}=\frac{40\times 5}{7}=\frac{200}{7}=28\frac{4}{7}%$