Define the variables

Let the original price be $P$ and original consumption be $C$. The initial expenditure is $E = P \times C$. After a $25\%$ price increase, the new price is $P' = 1.25P$.

$P' = P(1 + \frac{25}{100}) = 1.25P$

Set up the expenditure equation

Since expenditure must remain the same, $P \times C = P' \times C'$. Substitute $P' = 1.25P$ to find the new consumption $C'$.

$P \times C = 1.25P \times C' \implies C' = \frac{C}{1.25}$

Calculate the percentage reduction

The reduction in consumption is $C - C' = C - \frac{C}{1.25} = C(1 - 0.8) = 0.2C$. Expressing this as a percentage of original consumption $C$ gives $20\%$.

$\text{Reduction}\% = \frac{0.2C}{C} \times 100 = 20\%$