The price of an article is increased by 20% .By what percentage must its consumption be reduced so that the expenditure on it reduces by 10% ?

Options

A. `20%`
B. `30%`
C. `25%`
D. `15%`

Explanation

To solve the problem step by step, we will break down the process of calculating the percentage reduction in consumption required after a price increase.

### Step-by-Step Solution:

1. **Define Variables**:
- Let the original price of the article be \( x \).
- Let the original consumption of the article be \( y \).
- Therefore, the original expenditure is given by:
\[ \text{Expenditure} = x \times y \]

2. **Calculate the New Price**:
- The price of the article is increased by 20%. Thus, the new price becomes:
\[ \text{New Price} = x + 0.2x = 1.2x \]

3. **Calculate the New Expenditure**:
- The expenditure is to be reduced by 10%. Therefore, the new expenditure will be:
\[ \text{New Expenditure} = \text{Original Expenditure} - 10\% \text{ of Original Expenditure} \]
\[ = xy - 0.1(xy) = 0.9xy \]

4. **Set Up the Equation**:
- The new expenditure can also be expressed in terms of the new price and new consumption (\( y' \)):
\[ \text{New Expenditure} = \text{New Price} \times \text{New Consumption} \]
\[ 0.9xy = (1.2x) \times y' \]

5. **Simplify the Equation**:
- Cancel \( x \) from both sides (assuming \( x \neq 0 \)):
\[ 0.9y = 1.2y' \]

6. **Solve for New Consumption**:
- Rearranging the equation gives:
\[ y' = \frac{0.9y}{1.2} \]
- Simplifying this:
\[ y' = 0.75y \]

7. **Calculate the Reduction in Consumption**:
- The reduction in consumption is:
\[ \text{Reduction} = y - y' = y - 0.75y = 0.25y \]
- To find the percentage reduction:
\[ \text{Percentage Reduction} = \left(\frac{0.25y}{y}\right) \times 100\% = 25\% \]

### Final Answer:
The consumption must be reduced by **25%**.

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