If the price of sugar is raised by 25%, find by how much percent a householder must reduce his consumption of sugar so as not to increase his expenditure?

Options

A. 10
B. 20
C. 18
D. 25

Answer

To solve the problem, we need to find out how much a householder must reduce his consumption of sugar when the price of sugar increases by 25%, in order to keep his expenditure constant.

### Step-by-Step Solution:

1. **Understand the Initial Situation:**
Let's assume the initial price of sugar is \( P \) (in any currency, say Rs). The initial expenditure on sugar can be expressed as:
\[ \text{Expenditure} = \text{Price} \times \text{Quantity} \]
Let the initial quantity of sugar purchased be \( Q \). Therefore, the initial expenditure is:
\[ \text{Expenditure} = P \times Q \]

2. **Calculate the New Price After Increase:**
If the price of sugar is raised by 25%, the new price \( P' \) will be:
\[ P' = P + 0.25P = 1.25P \]

3. **Set Up the Equation for Constant Expenditure:**
To maintain the same level of expenditure after the price increase, the new quantity \( Q' \) of sugar that can be purchased must satisfy:
\[ \text{New Expenditure} = P' \times Q' = \text{Initial Expenditure} \]
Substituting the values, we get:
\[ 1.25P \times Q' = P \times Q \]

4. **Solve for the New Quantity \( Q' \):**
Dividing both sides by \( P \):
\[ 1.25Q' = Q \]
Now, solving for \( Q' \):
\[ Q' = \frac{Q}{1.25} = Q \times \frac{1}{1.25} = Q \times 0.8 \]

5. **Calculate the Reduction in Consumption:**
The reduction in consumption can be calculated as:
\[ \text{Reduction} = Q - Q' = Q - 0.8Q = 0.2Q \]

6. **Find the Percentage Reduction:**
The percentage reduction in consumption is given by:
\[ \text{Percentage Reduction} = \left(\frac{\text{Reduction}}{Q}\right) \times 100 = \left(\frac{0.2Q}{Q}\right) \times 100 = 20\% \]

### Final Answer:
The householder must reduce his consumption of sugar by **20%** in order not to increase his expenditure.

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