Assume Initial Values

Let the initial price of petrol be $100$ and initial consumption be $100$ units. The initial expenditure is $100 \times 100 = 10000$.

$\text{Initial Expenditure} = 100 \times 100 = 10000$

Calculate New Price

Since the price increases by $20\%$, the new price becomes $120$.

$\text{New Price} = 100 + 20 = 120$

Equate Expenditure

To keep the expenditure constant at $10000$, let the new consumption be $x$. Therefore, $120 \times x = 10000$.

$x = \frac{10000}{120} = \frac{250}{3} = 83.33$

Calculate Percentage Reduction

The reduction in consumption is $100 - 83.33 = 16.67\%$, which is equal to $16.66\%$.

$\text{Reduction} = 100 - 83.33 = 16.66\%$