Question

If the price of a commodity is increased by $50\%,$ then by what fraction must its consumption be reduced to keep the same expenditure on its consumption?

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{1}{5}$
• D. $\frac{3}{5}$

Answer 1

The correct option is B $\frac{1}{3}$

Let the initial price of the commodity be $x.$
Then, after $50\%$ increase in price, it will become,
$x+x\times \frac{50}{100}=1.5x$
Now, we have to reduce the consumption to keep expenditure $x.$
Increase in price $=1.5x-x=0.5x$
We have to reduce the consumption by $\frac{0.5x}{1.5x}=\frac{1}{3}$ unit.