Question

A number has increased by 20%. By what percentage the new number is decreased so that the number restores the original value?
A.15.34%
B.16.03%
C.16.67%
D.17.23%

Answer 1

Hint: In this question, we are going to suppose the original number as x and then calculate 20% of x. Then we will need to find the number to be subtracted from the new number in order to restore it to the original value. After finding that number, simply convert that number into percentage.

Complete step by step solution:
We are given a number, which is firstly increased by 20%.
Let this number be x.
20 % of x $ = \dfrac{{20}}{{100}}x $
  $ = \dfrac{x}{5} $
Now, the number(x) is increased by 20% of x.
New number $ = x + \dfrac{x}{5} $
 $ = \dfrac{{6x}}{5} $
Now, we want to find the percentage decrease so that this new number restores to its original value.
That means we have to convert $ \dfrac{{6x}}{5} $ to $ x $ again.
For that we have to subtract $ x $ from $ \dfrac{{6x}}{5} $ .
Therefore, $ \dfrac{{6x}}{5} - x = \dfrac{x}{5} $ .
Hence, we need to decrease the new number by $ \dfrac{x}{5} $ to get back the original value that is $ x $ .
But, we are asked to find it in terms of percentage.
To find the percentage decrease, divide $ \dfrac{x}{5} $ by $ \dfrac{{6x}}{5} $ and then multiply by 100.
Therefore, Percentage decrease $ = \dfrac{{\dfrac{x}{5}}}{{\dfrac{{6x}}{5}}} \times 100 $
 $
   = \dfrac{x}{5} \times \dfrac{5}{{6x}} \times 100 \\
   = \dfrac{{100}}{6} \\
   = 16.67 \;
  $
Hence, if a number is increased by 20%, it should be decreased by 16.67% in order to restore the real value.
Therefore, the correct answer is option C.
So, the correct answer is “Option C”.

Note: We can also suppose the number as 100 instead of x.
If this number is increased by 20%, then the new number will be 120. Now, subtract 100 from 120 to find the number to be decreased from the new number to restore it to original value. Now, convert this number into percentage.
Original number $ = 100 $
New number $ = 120 $
Decrease number $ = 120 - 100 $
 $ = 20 $
Percentage decrease $ = \dfrac{{20}}{{120}} \times 100 $
  $ = 16.67\% $