Question

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

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

Hint:

To keep expenditure constant when price increases, consumption must decrease in inverse proportion. Use the ratio of old price to new price.

Answer 1

The Correct Option is D

Let the family earlier consume $x$ kg of wheat when the price was \rupee 24.
So, total expenditure $= 24x$
Now price increases to \rupee 27, and expenditure remains the same, so
New quantity $= \dfrac{24x}{27}$
Reduction in consumption $= x - \dfrac{24x}{27} = x \left(1 - \dfrac{24}{27}\right) = x \left(\dfrac{3}{27}\right) = \dfrac{x}{9}$
Percentage reduction $= \dfrac{\dfrac{x}{9}}{x} \times 100 = \dfrac{1}{9} \times 100 = \boxed{11.1%}$