Price of sugar rises by 20%. By how much percent should the consumption of sugar be reduced. so that the expenditure does not change?

Options

A. 0.2
B. 0.1
C. 16 `2/3` %
D. 0.15

Answer

To solve the problem of how much the consumption of sugar should be reduced so that the expenditure remains unchanged after a 20% increase in price, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Price, Consumption, and Expenditure:**
- Expenditure = Price × Consumption
- If the price increases, the consumption must decrease to keep the expenditure constant.

2. **Calculate the New Price After the Increase:**
- Let the original price of sugar be \( P \).
- After a 20% increase, the new price \( P' \) is:
\[ P' = P + 0.20P = 1.20P \]

3. **Set Up the Equation for Constant Expenditure:**
- Let the original consumption be \( C \).
- The original expenditure is:
\[ E = P \times C \]
- The new consumption after the price increase (let's call it \( C' \)) must satisfy:
\[ E = P' \times C' \]
- Substituting the new price:
\[ P \times C = 1.20P \times C' \]

4. **Simplify the Equation:**
- We can divide both sides by \( P \) (assuming \( P \neq 0 \)):
\[ C = 1.20C' \]
- Rearranging gives:
\[ C' = \frac{C}{1.20} \]

5. **Calculate the Reduction in Consumption:**
- The reduction in consumption is:
\[ \text{Reduction} = C - C' = C - \frac{C}{1.20} \]
- This simplifies to:
\[ \text{Reduction} = C \left(1 - \frac{1}{1.20}\right) = C \left(\frac{1.20 - 1}{1.20}\right) = C \left(\frac{0.20}{1.20}\right) = \frac{C}{6} \]

6. **Calculate the Percentage Reduction:**
- The percentage reduction is given by:
\[ \text{Percentage Reduction} = \left(\frac{\text{Reduction}}{C}\right) \times 100 = \left(\frac{C/6}{C}\right) \times 100 = \frac{1}{6} \times 100 \approx 16.67\% \]

### Final Answer:
The consumption of sugar should be reduced by approximately **16.67%** to keep the expenditure unchanged after a 20% increase in price.