Question

The price of sugar has increased by 20%. By what percent must consumption of sugar be decreased so that the expenditure on sugar may remain the same?

Answer 1

Hint: We first assume the consumption of sugar and the price of the sugar. We will find the increased price. Then from the total expenditure we find the new amount of sugar consumption of sugar. We will finally convert it percentage form.

Complete step-by-step answer:
Let us assume the consumption of sugar is $y$ Kg. The price of the sugar is $x$ Rs. per Kg.
The total price will be $xy$ Rs.
The price of sugar has increased by 20%. Therefore, the new price is
$x\left( 1+\dfrac{20}{100} \right)=\dfrac{120x}{100}=\dfrac{6x}{5}$ .
As the total expenditure on sugar may remain the same, we find the new use of sugar.
We get $\dfrac{xy}{\dfrac{6x}{5}}=\dfrac{5xy}{6x}=\dfrac{5y}{6}$.
The change of consumption reduces by $y-\dfrac{5y}{6}=\dfrac{y}{6}$.
The percentage change is $\dfrac{\dfrac{y}{6}}{y}\times 100=\dfrac{50}{3}$.
The consumption needs to be reduced by $\dfrac{50}{3}$%.
So, the correct answer is “Option B”.

Note: The value of the fraction is actually the unitary value of $\dfrac{50}{3}$ out of 100. Therefore, in percentage value we got $\dfrac{50}{3}$ as the percentage. Percentage deals with the ratio out of 100. The ratio value for both fraction and percentage is the same.