Identify Relation

Expenditure is the product of price and consumption: $\text{Expenditure} = \text{Price} \times \text{Consumption}$. For expenditure to remain constant, consumption is inversely proportional to price.

$P_1 \times C_1 = P_2 \times C_2$

Set up Values

Let initial price $P_1 = 100$ and initial consumption $C_1 = 100$. New price $P_2 = 125$.

$P_2 = 1.25 \times P_1$

Calculate New Consumption

Since expenditure is same, $100 \times 100 = 125 \times C_2 \implies C_2 = \frac{10000}{125} = 80$.

$C_2 = 80$

Find Percentage Reduction

Reduction in consumption = $100 - 80 = 20$, which corresponds to a $20\%$ reduction.

\text{Percentage Reduction} = \left(\frac{20}{100}\right) \times 100 = 20\