Understand the Relationship

Expenditure is the product of price and consumption, so Expenditure = Price $\times$ Consumption. To keep expenditure constant, price and consumption are inversely proportional.

$\text{Expenditure} = \text{Price} \times \text{Consumption}$

Set up the Price Ratio

Let the original price be 100. After a 20% increase, the new price becomes 120. The ratio of original price to new price is $100: 120$ or $5: 6$.

$\text{Price Ratio} = 5: 6$

Determine the Consumption Ratio

Since expenditure remains constant, the consumption ratio must be the inverse of the price ratio, which is $6: 5$.

$\text{Consumption Ratio} = 6: 5$

Calculate Percentage Reduction

Consumption drops from 6 units to 5 units, a reduction of 1 unit on an initial consumption of 6 units. Therefore, the percentage reduction is $\frac{1}{6} \times 100 = 16.67\%.$

$\text{Reduction} = \frac{6 - 5}{6} \times 100 = 16.67\%$