Question

Verma gets \[10\% \] more than Akbar, then Akbar gets
A. \[10\% \] less than Verma
B. \[9\% \] less than Verma
C. $9\dfrac{1}{{11}}\% $ less than Verma
D. \[10\% \] more than Verma

Answer 1

Hint: This question refers to the knowledge of percentage. The word percentage stands for “one hundredth part of a given number”. Percentage can be written as both decimal and fraction. To write a percentage as decimal, we can simply divide it by 100. For example, \[20\% \] can be written in fraction form as $\dfrac{{20}}{{100}}$ and in decimal form as 0.2.

Complete step-by-step answer:
Let the quantity Akbar gets be x units.
It is given that Verma gets \[10\% \] more than Akbar.
Therefore, Verma gets $x + \dfrac{{10x}}{{100}} = x + \dfrac{x}{{10}} = \dfrac{{11x}}{{10}}$ units.
Thus, Akbar gets $\dfrac{{11x}}{{10}} - x = \dfrac{x}{{10}}$ units less than Verma.
Now, for \[\% \] loss suffered by Akbar is given by $\dfrac{{\dfrac{x}{{10}}}}{{\dfrac{{11x}}{{10}}}} \times 100\% $
                                \[
   = \dfrac{1}{{11}} \times 100\% \\
   = \dfrac{{100}}{{11}}\% \\
   = 9\dfrac{1}{{11}}\% \\
 \]
Thus, Akbar gets \[9\dfrac{1}{{11}}\% \] less than Verma.
Option (C) is correct.

Note: In the above question, many students go wrong thinking that Akbar will get \[10\% \] less. But this is not the case in this question.
Here, first we have to find how much Verma gets and find the loss suffered by Akbar i.e. how much less Akbar gets as compared to Verma.
Then, we have to find the \[\% \] loss suffered by Akbar to get the correct answer.