Question

A number is increased by \[10\% \] and then decreased by \[10\% ,\] find the net increase or decrease per cent.
A) \[15\% \]
B) \[1\% \]
C) \[13\% \]
D) \[17\% \]

Answer 1

Hint: To solve this question, first we will assume that the number be \[100,\] and according to the question, we will first increase the number by \[10\% \], then we will decrease the number by \[10\% \]. Then after that we will find whether we get net increase or decrease per cent.

Complete step-by-step answer:
We have been given that a number is increased by \[10\% \] and then decreased by \[10\% ,\] we need to find the net increase or decrease per cent.
First of all, we will assume the number. So, let the number be \[100.\]
We have been given in the question that firstly, the number is increased by \[10{\text{ }}\% .\]
\[
   \Rightarrow 100{\text{ }} + {\text{ }}\dfrac{{\left( {100 \times 10} \right)}}{{100}} \\
   = 100{\text{ }} + {\text{ }}10 \\
   = 110 \\
\]
Then, we have been given in the question that secondly, the number is decreased by \[10\% .\]
\[
   \Rightarrow 110{\text{ - }}\dfrac{{\left( {110 \times 10} \right)}}{{100}} \\
   = 110{\text{ - 11}} \\
   = 99 \\
\]
Now, we know that, the net increase or decrease percentage \[ = \] (Original Number \[ - \] New Number)\[ \times \dfrac{{100}}{{100}}\]
where, the original number \[ = {\text{ }}100\]
and the new number \[ = {\text{ }}99\]
On putting the values in the above formula, we get
Net increase or decrease percentage
\[
   = {\text{ }}\left( {100{\text{ }} - {\text{ }}99} \right) \times \dfrac{{100}}{{100}} \\
   = (1) \times \dfrac{{100}}{{100}} \\
   = \dfrac{{100}}{{100}} \\
   = {\text{ }}1{\text{ }}\% \\
\]
So, we get the net decrease, which is \[1\% .\]
So, the correct answer is “Option B”.

Note: Students should take care, that in the solution, here we have assumed the number be \[100.\] Then we have applied the first condition i.e., increased by \[10\% \] on \[100,\] we get \[110.\] Now when we have applied the second condition i.e., decreased by \[10\% ,\] it is important for students to note that we have applied second condition on \[110\] not on \[100.\]