Question

The price of petrol goes up by 10%. By how much per cent must a motorist reduce the consumption of petrol so that the expenditure on it remains unchanged?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{consumption}\mathrm{of}\mathrm{petrol}\mathrm{originally}\mathrm{be}1\mathrm{unit}\mathrm{and}\mathrm{let}\mathrm{its}\mathrm{cost}\mathrm{be}\mathrm{Rs}100. \\ \mathrm{New}\mathrm{cost}\mathrm{of}1\mathrm{unit}\mathrm{of}\mathrm{petrol}=\mathrm{Rs}110 \\ \mathrm{Now},\mathrm{Rs}110\mathrm{will}\mathrm{yield}1\mathrm{unit}\mathrm{of}\mathrm{petrol}. \\ \mathrm{i}.\mathrm{e}.,\mathrm{Rs}100\mathrm{will}\mathrm{yield}\left(\frac{1}{110}\times 100\right),\mathrm{i}.\mathrm{e}.,\frac{10}{11}\mathrm{units}\mathrm{of}\mathrm{petrol}.\mathrm{} \end{gathered}$$

$\mathrm{Now},\mathrm{reduction}\mathrm{in}\mathrm{consumption}=\left(1-\frac{10}{11}\right)$$=\frac{1}{11}\mathrm{unit}$
$\mathrm{Percentage}\mathrm{of}\mathrm{reduction}=\left(\frac{1}{11}\times \frac{1}{1}\times 100\right)\%$$=9\frac{1}{11}\%$
$\therefore \mathrm{A}\mathrm{motorist}\mathrm{must}\mathrm{reduce}\mathrm{the}\mathrm{consumption}\mathrm{of}\mathrm{petrol}\mathrm{by}9\frac{1}{11}\%.$