If the price of a commodity increases by 35%, then by what percentage should a family reduce its consumption so that there is no increase in total expenditure?

Solution:

Let original price = $P$ and original consumption = $Q$

Original expenditure = $P \times Q$

After a 35% increase in price, new price = $1.35P$

To keep expenditure constant:
$P \times Q = 1.35P \times Q_{new}$

Cancel $P$:
$Q = 1.35 Q_{new}$

So,
$Q_{new} = \frac{Q}{1.35} = \frac{Q}{\frac{135}{100}} = \frac{100}{135}Q = \frac{20}{27}Q$

Reduction in consumption:

Reduction = $1 - \frac{20}{27} = \frac{7}{27}$

Percentage reduction:
$\frac{7}{27} \times 100 = 25\frac{25}{27}%$

✅ Final Answer: $25\frac{25}{27}%$