The price (per litre) of petrol increases by 60%. By what percent should its consumption be reduced such that the expenditure on it increases by 44% only?

Given:

The price (per litre) of petrol increases by 60%.

Expenditure on petrol is allowed to increase by only 44%.

Formula Used:

Let the initial price of petrol be ₹P per litre, and initial consumption be C litres.

Expenditure = Price × Consumption

New Expenditure = (1 + 44/100) × Initial Expenditure

New Price = (1 + 60/100) × Initial Price

To find the percentage reduction in consumption, use the formula:

Required Reduction (%) = $\left(1 - \frac{\text{New Consumption}}{\text{Initial Consumption}}\right) \times 100$

Calculation:

Let the initial expenditure be 100 (for simplicity).

Initial Expenditure = Price × Consumption = ₹P × C

New Expenditure = 144 (as it increases by 44%).

New Price = ₹P × 1.6 (as price increases by 60%).

New Consumption = New Expenditure / New Price

⇒ New Consumption = 144 / (1.6 × P)

⇒ New Consumption = 144 / 1.6

⇒ New Consumption = 90% of Initial Consumption.

Reduction in Consumption = Initial Consumption - New Consumption

⇒ Reduction = 100% - 90%

⇒ Reduction = 10%.

The consumption should be reduced by 10%.