If the price of sugar is increased by 10%, then by how much percent consumption should be reduced so that the expenditure remains the same?

Options

A. 9.09
B. 10
C. 12.5
D. 20

Answer

To solve the problem, we need to determine how much the consumption of sugar should be reduced in order to keep the expenditure constant after a 10% increase in the price of sugar.

### Step-by-Step Solution:

1. **Understand the relationship between price, consumption, and expenditure**:
- Expenditure (E) is given by the formula:
\[ E = \text{Price} \times \text{Consumption} \]
- If the price increases, to maintain the same expenditure, consumption must decrease.

2. **Let the original price of sugar be \( P \)** and the original consumption be \( C \)**:
- Therefore, the initial expenditure can be expressed as:
\[ E = P \times C \]

3. **Calculate the new price after a 10% increase**:
- A 10% increase in price means the new price \( P' \) is:
\[ P' = P + 0.1P = 1.1P \]

4. **Set up the equation for the new expenditure**:
- To keep the expenditure the same after the price increase, the new consumption \( C' \) must satisfy:
\[ E = P' \times C' \]
- Substituting for \( E \) gives:
\[ P \times C = 1.1P \times C' \]

5. **Simplify the equation**:
- Dividing both sides by \( P \) (assuming \( P \neq 0 \)):
\[ C = 1.1 \times C' \]
- Rearranging gives:
\[ C' = \frac{C}{1.1} \]

6. **Calculate the reduction in consumption**:
- The reduction in consumption \( R \) is:
\[ R = C - C' = C - \frac{C}{1.1} = C \left(1 - \frac{1}{1.1}\right) \]
- Simplifying further:
\[ R = C \left(\frac{1.1 - 1}{1.1}\right) = C \left(\frac{0.1}{1.1}\right) \]

7. **Calculate the percentage reduction**:
- The percentage reduction in consumption is given by:
\[ \text{Percentage Reduction} = \frac{R}{C} \times 100 = \frac{C \left(\frac{0.1}{1.1}\right)}{C} \times 100 \]
- This simplifies to:
\[ \text{Percentage Reduction} = \frac{0.1}{1.1} \times 100 \approx 9.09\% \]

### Final Answer:
The consumption should be reduced by approximately **9.09%** to keep the expenditure the same after a 10% increase in the price of sugar.

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