Question

If the price of sugar is increased by $25\% $ today; by what percent should it be decreased tomorrow to bring the price back to the original?
\[
  A.{\text{ }}25\% \\
  B.{\text{ }}24\% \\
  C.{\text{ }}22\% \\
  D.{\text{ }}20\% \\
 \]

Answer 1

Hint- In order to solve such questions where the exact value of the item is not given, assume some unknown variable as the price of the item and then perform all the calculations in terms of the same variable. Whenever you will need to find the percentage automatically the unknown variable will be cancelled out.

Complete step-by-step answer:
Let us consider the initial price of sugar to be $x$ .
Now, if the price was increased today by $25\% $, then the new price is:
Old price + $25\% $ of old price
$
   = x + 25\% {\text{ }}of\left( x \right) \\
   = x + \dfrac{{25}}{{100}}x \\
   = x + 0.25x \\
   = 1.25x \\
 $
Now the new price is $1.25x$ , in order to make the price older one we need to make it $x$.
$ \Rightarrow 1.25x - x = 0.25x$
So $0.25x$ price must be subtracted in order to make the price old one.
So percentage reduction in the price
$
   = \dfrac{{{\text{reduction in price}}}}{{{\text{new price}}}} \times 100 \\
   = \dfrac{{0.25x}}{{1.25x}} \times 100 \\
   = \dfrac{{0.25}}{{1.25}} \times 100 \\
   = 20\% \\
 $
Hence, the 20 percent price must be reduced in order to make the price older one.
So option D is the right option.

Note- In order to solve such problems related to prices, consider in terms of some unknown variable then deal in the same variable. This type of problem can also be solved by considering the initial price to be 100 and then proceeding in a similar way. That method is best to use in competitive exams as the number of steps are reduced and answers come fast by simple calculation.