Question

Wheat is now being sold at Rs. 27 per kg. During last month its cost was Rs. 24 per kg. Find by how much per cent a family reduces its consumption so as to keep the expenditure fixed.

• A. 10.2%
• B. 12.1%
• C. 12.3%
• D. 11.1%

Answer 1

The Correct Option is D

To determine the percentage by which a family needs to reduce its consumption to maintain the same expenditure despite an increase in wheat price, we can approach this problem by comparing the initial and new expenditure based on consumption.

Step 1: Define Initial Conditions
Let the initial consumption of wheat be x kg. The initial price is Rs. 24 per kg, so the initial expenditure is:

Initial Expenditure = 24x Rs

Step 2: Define Conditions After Price Change
The new price of wheat is Rs. 27 per kg, and we need to maintain the expenditure constant, so:

New Expenditure = 27y Rs

where y is the new consumption in kg.

Step 3: Equate the Expenditures
Since the expenditure is fixed, equating the initial and new expenditures gives us:

\(24x = 27y\)

Step 4: Express Consumption Reduction
Rearrange the equation to find the relationship between y and x:

\(y = \frac{24x}{27}\)

The reduction in consumption is given by:

\(x - y = x - \frac{24x}{27}\)

\(=\left(x - \frac{24x}{27}\right) = x\left(1 - \frac{24}{27}\right)\)

\(= x\cdot\frac{3}{27} = x\cdot\frac{1}{9}\)

Step 5: Calculate Percentage Reduction
The percentage reduction in consumption is:

\(\left(\frac{x/9}{x}\right) \cdot 100\% = \frac{1}{9} \cdot 100\% \approx 11.11\%\)

Conclusion: The family needs to reduce its wheat consumption by approximately 11.1% to keep the expenditure fixed.