Question

If Anil’s salary is 20% less than Raju’s salary, then by what percent is Raju’s salary more than that of Anil?

Answer 1

Hint: Start by letting Anil’s salary to be Rs. x and Raju’s salary be Rs. y. It is given that Anil’s salary is 20% less than that of Raju, which means that (y-x) is 20% of Raju’s salary. So, form an equation using this data to get a relation between x and y. The % by which Raju’s salary is more than that of Anil’s is given by (y-x) divided by x and the result multiplied by 100 to convert it to percent.

Complete step-by-step answer:
Let us start the solution to the above question by letting Anil’s salary to be Rs. x and Raju’s salary be Rs. y.
Now it is given that Anil’s salary is 20% less than that of Raju and we know that the difference in the salary is Rs. (y-x). So, we can say that (y-x) is 20% of Raju’s salary. If we represent this mathematically, we get
  $ \dfrac{y-x}{y}\times 100=20 $
  $ \Rightarrow \left( 1-\dfrac{x}{y} \right)=\dfrac{20}{100} $
  $ \Rightarrow 1-\dfrac{20}{100}=\dfrac{x}{y} $
  $ \Rightarrow \dfrac{80}{100}=\dfrac{x}{y}........(i) $
Now, we are asked to find the % by which Raju’s salary is more than that of Anil’s. The difference in salary in this case is also Rs. (y-x), but we have to find the % with respect to Anil’s salary, i.e., Rs. x.
\[\text{ }\!\!\%\!\!\text{ by which Rajus salary is more than that of Anils}=\dfrac{y-x}{x}\times 100\]
\[\Rightarrow \text{ }\!\!\%\!\!\text{ by which Rajus salary is more than that of Anils}=\left( \dfrac{y}{x}-1 \right)\times 100\]
\[\Rightarrow \text{ }\!\!\%\!\!\text{ by which Rajus salary is more than that of Anils}=\left( \dfrac{1}{\dfrac{y}{x}}-1 \right)\times 100\]
If we use equation (i) and substitute $ \dfrac{80}{100}=\dfrac{x}{y} $ , we get
\[\text{ }\!\!\%\!\!\text{ by which Rajus salary is more than that of Anils}=\left( \dfrac{100}{80}-1 \right)\times 100\]
\[\Rightarrow \text{ }\!\!\%\!\!\text{ by which Rajus salary is more than that of Anils}=\dfrac{20}{80}\times 100=25\%\] .
Hence, the answer to the above question is 25%.

Note: The most important thing in the above question is to recognise that with respect to whose salary is the % difference is being defined, for example: in the first case where the salary of Anil was 20% less than Raju is defined with respect to Raju’s salary. The other thing you should be very careful about is the calculation part, where students generally make mistakes.