In a new budget, the price of petrol rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
20%
To solve the problem of determining by how much percent a person must reduce his consumption of petrol to ensure his expenditure does not increase despite a price rise, let's go through the solution step-by-step.
Given:
- Initial price of petrol = \( P \)
- New price of petrol after a 25% increase = \( P + 0.25P = 1.25P \)
Let the initial consumption be \( C \) (liters). Therefore, the initial expenditure is given by:
\(E_{\text{initial}} = P \times C\)
For the expenditure to remain unchanged after the price hike, the new expenditure should be equal to the initial expenditure:
\(E_{\text{new}} = 1.25P \times C_{\text{new}} = P \times C\)
Solving the above equation for \( C_{\text{new}} \):
\(C_{\text{new}} = \frac{P \times C}{1.25P} = \frac{C}{1.25}\)
This can be written as:
\(C_{\text{new}} = 0.8C\)
Thus, the consumption must be reduced to 80% of the original.
The percentage reduction in consumption is calculated as:
\(\text{Percentage Reduction} = \frac{C - C_{\text{new}}}{C} \times 100\)
Substituting the known values:
\(\text{Percentage Reduction} = \frac{C - 0.8C}{C} \times 100 = \frac{0.2C}{C} \times 100 = 20\%\)
Therefore, the person must reduce his consumption by 20% to maintain the same expenditure.
Given options: 10%, 15%, 20%, 25%
Correct Answer: 20%
This ties with the given solution and answers the question accurately. Thus, 20% is the correct and justified choice.
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