The price of petrol increases by 10%, by what percent must the consumption be decreased to keep the expenditure same?

Questions : The price of petrol increases by 10%, by what percent must the consumption be decreased to keep the expenditure same?

Answer:  

 

Shortcut Formula:

$$\text{Percentage Decrease} = \frac{\text{Percentage Increase} \times 100}{\text{Percentage Increase} + 100}$$

Given:

• Price increase = 10%

Applying the formula:

$$\text{Percentage Decrease} = \frac{10 \times 100}{10 + 100}$$ $$= \frac{1000}{110} \approx 9.09\%$$

Final Answer:

Consumption must be decreased by approximately 9.09%.

Alternative 

1. Understand the Relationship

• Price and Consumption: When the price of a commodity increases, the consumption must decrease to keep the expenditure the same.
• Inverse Proportion: The percentage increase in price and the percentage decrease in consumption are related by an inverse proportion.

2. Set up the Calculation

Let the original price of petrol be Rs. 100 (for easy calculation).

• New price: 100 + (10% of 100) = Rs. 110

Now, let the original consumption be 100 units (again, for easy calculation).

• Original expenditure: 100 * 100 = Rs. 10,000

To keep the expenditure the same, the new consumption (let's call it 'x') must satisfy:

• New expenditure: 110 * x = 10,000

3. Solve for x

• x = 10,000 / 110
• x ≈ 90.91 units

4. Calculate the Percentage Decrease

• Decrease in consumption = 100 - 90.91 = 9.09 units
• Percentage decrease = (Decrease in consumption / Original consumption) * 100
• Percentage decrease = (9.09 / 100) * 100
• Percentage decrease ≈ 9.09%

Answer: The consumption of petrol must be decreased by approximately 9.09% to keep the expenditure the same.

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