The price (per litre) of petrol increases by 50%. By what percent should its consumption be reduced such that the expenditure on it increases by 14% only?

Formula used:

Percentage Reduction in Consumption = \(\dfrac{\text{Initial Consumption - Reduced Consumption}}{\text{Initial Consumption}} \times 100\)

Calculation:

Let the initial price of petrol be ₹100 and consumption be 100 litres.

Initial expenditure = Price × Consumption

Let the reduced consumption be x litres.

New expenditure = New Price × Reduced Consumption

New expenditure = 114% of Initial expenditure

Initial expenditure = 100 × 100 = ₹10,000

New price = 100 + 50 = ₹150 per litre

New expenditure = ₹10,000 × \(\dfrac{114}{100}\) = ₹11,400

New expenditure = New Price × Reduced Consumption

⇒ ₹11,400 = ₹150 × x

⇒ x = \(\dfrac{11400}{150}\) = 76 litres

Percentage reduction in consumption:

⇒ \(\dfrac{100 - 76}{100} \times 100\)

⇒ \(\dfrac{24}{100} \times 100\)

⇒ 24%

∴ The correct answer is option (2).