In Dew government policy, the price of onion is raised by 35%. By what percentage should a person reduce onion consumption so that the expenditure on it does not increase?
A. `25%`
B. `29%`
C. `26%`
D. `33%`

Options

A. B
B. A
C. D
D. C

Answer

To solve the problem step by step, we need to determine by what percentage a person should reduce onion consumption to keep the expenditure constant after a 35% increase in the price of onions.

### Step-by-Step Solution:

1. **Understanding the Price Increase**:
- Let the original price of onions be \( P = 100 \) (for simplicity).
- After a 35% increase, the new price \( P' \) becomes:
\[ P' = P + 0.35P = 100 + 35 = 135 \]

2. **Setting Up the Expenditure Equation**:
- Let the original quantity of onions consumed be \( Q \).
- The original expenditure \( E \) on onions is given by:
\[ E = P \times Q = 100 \times Q \]
- After the price increase, if the new quantity consumed is \( Q' \), the new expenditure \( E' \) is:
\[ E' = P' \times Q' = 135 \times Q' \]

3. **Equating the Expenditures**:
- To keep the expenditure the same, we set \( E = E' \):
\[ 100Q = 135Q' \]

4. **Finding the New Quantity**:
- Rearranging the equation gives:
\[ Q' = \frac{100Q}{135} \]
- Simplifying this, we find:
\[ Q' = \frac{20Q}{27} \]

5. **Calculating the Reduction in Consumption**:
- The reduction in consumption \( R \) is:
\[ R = Q - Q' = Q - \frac{20Q}{27} \]
- This can be simplified to:
\[ R = \frac{27Q}{27} - \frac{20Q}{27} = \frac{7Q}{27} \]

6. **Finding the Percentage Reduction**:
- The percentage reduction in consumption is given by:
\[ \text{Percentage Reduction} = \left(\frac{R}{Q} \times 100\right) = \left(\frac{\frac{7Q}{27}}{Q} \times 100\right) = \frac{7}{27} \times 100 \]
- Calculating this gives:
\[ \frac{700}{27} \approx 25.92\% \]

7. **Rounding Off**:
- Rounding \( 25.92\% \) gives approximately \( 26\% \).

### Conclusion:
The percentage by which a person should reduce onion consumption to keep the expenditure constant after a 35% price increase is approximately **26%**.