Question

For an amount, explain why, a \[20\% \] increase followed by a \[20\% \] decrease is less than the original amount.

Answer 1

Hint: In the above given question, we are given an original amount which is first increased by a factor of \[20\% \] and then it is followed by a decrease of a factor \[20\% \] . We have to explain the reason behind the fact that the obtained amount after the increase followed by the same percentage of decrease is less than the original amount.

Complete step by step answer:
Given that, the original amount is first increased by \[20\% \] and then further decreased by \[20\% \] .
We have to explain why the obtained amount after the increase and decrease is less than the original amount.
Since the original amount is whole hence we can say that the percentage of the original amount can be written as \[100\% \] .
Now, if the original amount is \[100\% \] ,
Then after an increase of \[20\% \] the obtained amount will be,
\[ \Rightarrow 100\% + \left( {\dfrac{{20}}{{100}} \times 100\% } \right)\]
That gives us,
\[ \Rightarrow 100\% + 20\% \]
Hence,
\[ \Rightarrow 120\% \]
i.e. the obtained amount is \[120\% \] of the original amount.
Now, if the obtained amount, i.e. \[120\% \] is further decreased by \[20\% \] ,
Then the new final obtained amount will be equal to,
\[ \Rightarrow 120\% - \left( {\dfrac{{20}}{{100}} \times 120\% } \right)\]
That gives us,
\[ \Rightarrow 120\% - 24\% \]
Hence,
\[ \Rightarrow 96\% \]
Therefore, the final obtained amount is only \[96\% \] of the original amount.
That means the obtained amount after the successive increase and decrease of \[20\% \] , is exactly \[4\% \] less than the original amount.

Note:
The successive increase and decrease of \[20\% \] of an original amount gives the obtained amount less than the original amount because the increase is calculated on the original amount which is lesser than the amount obtained after an increase of \[20\% \] . Whereas the decrease of \[20\% \] is calculated on the increased amount, where its \[20\% \] is larger than the \[20\% \] of the original amount, and hence as a result the final amount is decreased lower than the original amount.