Question

If the salary of X is 20 % more than the salary of Y, then by how much percentage is the salary of Y less than X?
A. 25
B. 20
C. $ \dfrac{50}{3} $
D. $ \dfrac{65}{4} $

Answer 1

Hint:We will first assume the salary of Y to be a variable, then we will find the salary of X in terms of the assumed salary of Y. After that, we will find the percentage of salary of Y that is less than X, by using the formula, % of Y’s salary less than X = $ \dfrac{\text{Salary of X-Salary of Y}}{\text{Salary of X}}\times 100 $ .

Complete step-by-step answer:
We have been given that the salary of X is 20 % more than the salary of Y and we have been asked to find the percentage by which Y’s salary is less than X. Let us suppose the salary of Y as Rs. S. So, according to the question, the salary of X is,
 $ \begin{align}
  & S+20\text{ }\!\!\%\!\!\text{ of }S \\
 & \Rightarrow S+\dfrac{20}{100}\times S \\
 & \Rightarrow S+\dfrac{S}{5} \\
 & \Rightarrow \dfrac{5S+S}{5} \\
 & \Rightarrow \dfrac{6S}{5} \\
\end{align} $
So, we get the salary of X as equal to $ \dfrac{6S}{5} $ . We know that the percentage of salary of Y less than that of X is given by, $ \dfrac{\text{Salary of X-Salary of Y}}{\text{Salary of X}}\times 100 $ . We have the salary of X = $ \dfrac{6S}{5} $ and the salary of Y = S. So, applying it in the formula, we will get the percentage as,
 $ \begin{align}
  & =\dfrac{\dfrac{6S}{5}-S}{\dfrac{6S}{5}}\times 100 \\
 & \Rightarrow \dfrac{6S-5S}{5\times \dfrac{6S}{5}}\times 100 \\
 & \Rightarrow \dfrac{S}{6S}\times 100 \\
 & \Rightarrow \dfrac{50}{3}\% \\
\end{align} $
Hence, we get the percentage by which Y’s salary is less than X as $ \dfrac{50}{3}\% $ .
Therefore, the correct answer is option C.

Note: We should remember that we have to find the percentage with respect to X, so we divide the difference of salary with the salary of X. Sometimes we make the mistake and divide it by the salary of Y. We can also use the difference of the salary of X and Y, while calculating the percentage of Y’s salary less than X as it will save a lot of time.