Question

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

Answer 1

Hint: As we know that the expenditure done on the sugar will be the same as the product of the current rate of the sugar or we can say that the amount of sugar consumed. So by using the percentage formula and framing the equation, we will solve this problem
Formula used:
The formula for finding the $ x $ percentage of any item will be
 $ \dfrac{x}{{100}} \times {\text{ item}} $
Here, $ x $ will be the price and the item will be the quantity.

Complete step-by-step answer:
So according to the question, let us assume that the price of $ x{\text{ kg}} $ sugar will be $ Rs.100 $
Since there is an increase in price at $ 20\% $
Hence, the new price will be
 $ \Rightarrow Rs.\left( {100 + 20} \right) $
And on adding the above, we get
 $ \Rightarrow Rs.120 $
So for $ Rs.120 $ , obtained sugar will be equal to $ x{\text{ kg}} $
Therefore, for $ Rs.100 $ , obtained sugar will be calculated by using the formula of percentage
 $ \Rightarrow \dfrac{x}{{120}} \times 100kg $
And on solving it, we get
 $ \Rightarrow \dfrac{{5x}}{6}kg $
So from this, we can say that the original consumption will be $ x{\text{ kg}} $ and the new consumption will be $ \dfrac{{5x}}{6}kg $ .
Therefore, for the decrease or we can say the change in consumption will be equal to
 $ \Rightarrow x - \dfrac{{5x}}{6} $
And on solving it by taking the LCM, we get
 $ \Rightarrow \dfrac{x}{6} $
So the percentage required for a decrease in the consumption will be
 $ \Rightarrow \dfrac{x}{{6x}} \times 100 $
So the like term will cancel each other and taking the fraction into simplest form, we have
 $ \Rightarrow \dfrac{{50}}{3}\% $
And it will be equal to $ 16\dfrac{2}{3}\% $ .
Hence, $ 16\dfrac{2}{3}\% $ the decrease in the consumption of sugar.
So, the correct answer is “$ 16\dfrac{2}{3}\% $”.

Note: So while solving this type of question can be solved just by using the concepts. If our percentage concept is clear then we can easily solve it. Also, we should note that the sugar expenditure will be equal to the product of the current price of the sugar.