If food prices go up by 10%, by how much should a man reduce his consumption so as not to Increase his expenditure?

Options

A. 9 `1/11` %
B. 0.1
C. 11 `1/9` %
D. The data is not sufficient.

Answer

To solve the problem of how much a man should reduce his consumption when food prices increase by 10% in order to keep his expenditure constant, we can follow these steps:

### 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 expenditure is to remain constant, any increase in price must be offset by a decrease in consumption.

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

3. **Calculate the new price after a 10% increase**:
- If the price increases by 10%, the new price \( P' \) will be:
\[ P' = P + 0.10P = 1.10P \]

4. **Set up the equation for constant expenditure**:
- To keep the expenditure constant after the price increase, we have:
\[ E = P' \times C' \]
- Substituting \( P' \) into the equation gives:
\[ P \times C = 1.10P \times C' \]

5. **Simplify the equation**:
- Dividing both sides by \( P \) (assuming \( P \neq 0 \)):
\[ C = 1.10 \times C' \]
- Rearranging this gives:
\[ C' = \frac{C}{1.10} \]

6. **Calculate the reduction in consumption**:
- The reduction in consumption \( R \) is:
\[ R = C - C' = C - \frac{C}{1.10} = C \left(1 - \frac{1}{1.10}\right) \]
- Simplifying this:
\[ R = C \left(\frac{1.10 - 1}{1.10}\right) = C \left(\frac{0.10}{1.10}\right) = \frac{C}{11} \]

7. **Calculate the percentage reduction**:
- The percentage reduction in consumption is given by:
\[ \text{Percentage Reduction} = \left(\frac{R}{C}\right) \times 100 = \left(\frac{\frac{C}{11}}{C}\right) \times 100 = \frac{100}{11} \approx 9.09\% \]

### Final Answer:
The man should reduce his consumption by approximately **9.09%** to keep his expenditure constant after a 10% increase in food prices.