Question

If the price of a commodity is increased by $ 50\% $ . By what fraction must its consumption be reduced so as to keep the same expenditure on its consumption.
A. $ \dfrac{1}{4} $
B. $ \dfrac{1}{3} $
C. $ \dfrac{1}{2} $
D. $ \dfrac{2}{3} $

Answer 1

Hint: It is very imperative and exceedingly simple to understand that when the price of a commodity increases we have to likewise decrease its consumption in order to keep the expenditure the same. The question asks us to solve when the price of the commodity is increased by $ 50\% $ , by what fraction should we decrease its consumption to keep the same expenditure. We will first take a sample commodity with a simple price say $ Rs.100 $ . Then solve it to see what effect it has on our expenditure.

Complete step-by-step answer:
Let us take the price of the commodity as $ Rs.100 $ and its consumption by $ 1 $ so they spend $ Rs.100 $ .
The question says the price increases by $ 50\% $ ,
The price of the commodity now becomes $ Rs.150 $ .
The expenditure has to remain same, so they will still spend $ Rs.100 $ , the consumption will now become,
 $ \Rightarrow \dfrac{{100}}{{150}} $ ,
 $ \Rightarrow \dfrac{2}{3} $
Thus the current consumption is $ \dfrac{2}{3} $ of the previous consumption. The question asks by what fraction it reduces so that will be given by,
 $ original{\text{ }}consumption - current{\text{ }}consumption $
 $ \Rightarrow 1 - \dfrac{2}{3} $
 $ \Rightarrow \dfrac{1}{3} $
So the consumption decreases by one-third, since the only option which is the same as this is B. hence B. is the correct option.
So, the correct answer is “Option B”.

Note: In case it has asked what is the current consumption instead of the fraction it reduced by our desired fraction would have been $ \dfrac{2}{3} $ which would have given us the option D. as correct. The use of the word ‘by’ and ‘to’ has to be kept in mind in order to prevent inadvertent loss of marks, when to is asked the answer is current consumption, but when by is asked it means the fraction by which it decreases.