Question

The price of sugar is increased by $20\%$. As a result, a family decreases its consumption by $25\%$. The expenditure of the family on sugar will be decreased by

Answer 1

Finding the decrease in expenditure:

Let the old price of sugar be $₹100$ and family consumed $100$ units of sugar.

The price of sugar is increased by $20\%$.

Increase in price $=20\%\times 100=\frac{20}{100}\times 100=₹20$

New price $=\mathrm{Old}\mathrm{price}+\mathrm{Increas}e\mathrm{in}\mathrm{price}=100+20=₹120$

Family decreased the consumption of sugar by $25\%$.

Decrease in consumption$=25\%\times 100=\frac{25}{100}\times 100=25$ units.

New consumption$=\mathrm{Old}\mathrm{consumption}-\mathrm{Decrease}\mathrm{in}\mathrm{consumption}=100-25=75$ units

$\begin{array}{rcl}\mathrm{Old}\mathrm{Expenditure}& =& \mathrm{Old}\mathrm{Price}\times \mathrm{Old}\mathrm{Consumption}\\ & =& 100\times 100\\ & =& ₹10000\end{array}$

$\begin{array}{rcl}\mathrm{New}\mathrm{Expenditure}& =& \mathrm{New}\mathrm{Price}\times \mathrm{New}\mathrm{Consumption}\\ & =& 120\times 75\\ & =& ₹9000\end{array}$

Hence, Decrease in expenditure on sugar

$$\begin{gathered} =\frac{\mathrm{old}\mathrm{expenditure}-\mathrm{new}\mathrm{expenditure}}{\mathrm{old}\mathrm{expenditure}}\times 100 \\ =\frac{10000-9000}{10000}\times 100 \\ =\frac{1000}{10000}\times 100 \\ =\frac{1}{10}\times 100 \\ =10\% \end{gathered}$$

Hence, the expenditure of the family on sugar will be decreased by $10\%$.