Question

If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?

• A. 10
• B. 12
• C. 8
• D. 6.67

Hint:

You can use the formula: \( \text{New Quantity} = \frac{100 + \text{% change in Expenditure}}{100 + \text{% change in Price}} \times \text{Old Quantity} \). Here, \( \frac{115}{125} \times 100 = 92 \), so the reduction is \( 100 - 92 = 8% \).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question involves finding the percentage reduction in consumption (quantity) when both the price of an item and the total expenditure on it change.


Step 2: Key Formula or Approach:
The core relationship is: \( \text{Expenditure} = \text{Price} \times \text{Quantity} \).
We can assume initial values of 100 for simplicity and calculate the new quantity based on the percentage changes in price and expenditure.


Step 3: Detailed Explanation:
Let the initial Price (\( P_1 \)) be Rs. 100 per unit.
Let the initial Quantity (\( Q_1 \)) be 100 units.
Initial Expenditure (\( E_1 \)) = \( 100 \times 100 = 10,000 \).
The price increases by 25%, so the new Price (\( P_2 \)) is:
\[ P_2 = 100 + 25% \text{ of } 100 = 125 \] Raj intends to spend only 15% more, so the new Expenditure (\( E_2 \)) is:
\[ E_2 = 10,000 + 15% \text{ of } 10,000 = 10,000 + 1,500 = 11,500 \] Now, we find the new Quantity (\( Q_2 \)) using the formula \( Q_2 = \frac{E_2}{P_2} \):
\[ Q_2 = \frac{11,500}{125} = 92 \text{ units} \] The reduction in quantity is \( Q_1 - Q_2 = 100 - 92 = 8 \text{ units} \).
Since the initial quantity was 100, the percentage reduction is simply 8%.


Step 4: Final Answer:
He will reduce the quantity of petrol purchased by 8%.