Question

If the cost of a commodity increases by 60%, by what fraction must its consumption be reduced so as to keep the expenditure same as before.

• A. $\frac{1}{5}$
• B. $\frac{1}{4}$
• C. $\frac{2}{5}$
• D. $\frac{1}{3}$

Answer 1

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

Let the initial price of the commodity and consumption be Rs. 100 and 100 respectively.
After 50% increase in price, It will become 100 + 50 = Rs. 150
Now, we have to reduce the consumption to keep expenditure 100.
$100\times 100=150\times x\Rightarrow x=100\times \frac{100}{150}=\frac{200}{3}$
% reduction $=\frac{[100-\left(\frac{200}{3}\right)]}{100}\times 100=33.33\%=\frac{1}{3}$