The price of sugar goes up by 20%. If a housewife wants the expenses on sugar to remain the same, she should reduce the consumption by

Options

A. `55(1)/(5)%`
B. `16(2)/(3)%`
C. `20%`
D. `25%`

Answer

To solve the problem, we need to understand how the increase in the price of sugar affects the quantity that a housewife can buy while keeping her total expenses the same.

### Step-by-Step Solution:

1. **Understand the Price Increase**:
The price of sugar has increased by 20%. This means if the original price of sugar is \( P \), the new price becomes:
\[ \text{New Price} = P + 0.20P = 1.20P \]

2. **Define the Original Consumption**:
Let the original quantity of sugar consumed be \( Q \). Therefore, the original expense on sugar is:
\[ \text{Original Expense} = P \times Q \]

3. **Calculate the New Expense**:
After the price increase, if the housewife wants to keep her expenses the same, she must adjust her consumption. Let the new quantity of sugar consumed be \( Q' \). The new expense will be:
\[ \text{New Expense} = 1.20P \times Q' \]

4. **Set the Expenses Equal**:
To keep the expenses the same, we set the original expense equal to the new expense:
\[ P \times Q = 1.20P \times Q' \]

5. **Cancel Out the Price**:
Since \( P \) is common in both sides and assuming \( P \neq 0 \), we can cancel it out:
\[ Q = 1.20 \times Q' \]

6. **Solve for New Consumption**:
Rearranging the equation gives:
\[ Q' = \frac{Q}{1.20} = \frac{Q}{\frac{6}{5}} = \frac{5Q}{6} \]

7. **Calculate the Reduction in Consumption**:
The reduction in consumption can be calculated as:
\[ \text{Reduction} = Q - Q' = Q - \frac{5Q}{6} = \frac{1Q}{6} \]

8. **Calculate the Percentage Reduction**:
To find the percentage reduction in consumption:
\[ \text{Percentage Reduction} = \left(\frac{\text{Reduction}}{Q}\right) \times 100 = \left(\frac{\frac{1Q}{6}}{Q}\right) \times 100 = \frac{1}{6} \times 100 \approx 16.67\% \]

### Final Answer:
The housewife should reduce her consumption of sugar by approximately **16.67%** to keep her expenses the same.