If price of commodity is increased by 50% by what fraction must its consumption be reduced so as to keep same expenditure on its consumption?

Let the initial price of the commodity be 100.

After 50% increase in price, It will become,
100 ------50% increase----> 150.
Now, we have to reduce the consumption to keep expenditure 100.

Increase in price= 150 - 100 = 50
We have to reduce the consumption,
$$\eqalign{ & = \frac{{50}}{{150}} \times 100 \cr & = \frac{1}{3}{\text{ or 33}}{\text{.33}}\% \cr} $$

Other Method:
Here, we use, Final product constant graphic.
100 ==50% up== 150===33.33% down===>100
Consumption Reduce = 33.33% = $$\frac{1}{3}$$