Question

Nancy obtained 426 marks out of 600 and the marks obtained by Rohit are 560 out of 800. Whose performance is better?

Answer 1

Hint: This question is based on the percentage. In this question the marks of two people are given and by using the percentage method we have to find the person whose performance is better as compared to the other person. In order to solve this question we find the percentage marks obtained by both Nancy and Rohit, and if the percentage of marks obtained by Nancy are greater than the percentage of marks obtained by Rohit then the performance of Nancy is better than Rohit or vice-versa.

Complete step-by-step answer:
Given:
Marks obtained by Nancy $ {x_1} = 426 $
Total marks available for Nancy $ {y_1} = 600 $
So, the percentage of the marks obtained by Nancy are given by-
\[
\Rightarrow \% {\rm{Marks obtained by Nancy = }}\dfrac{{{\text{Marks obtained by Nancy}}}}{{{\text{Total marks available for Nancy}}}} \times 100\\
\Rightarrow \% {\rm{Marks obtained by Nancy }} = \dfrac{{{x_1}}}{{{y_1}}} \times 100\\
\Rightarrow \% {\rm{Marks obtained by Nancy }} = \dfrac{{426}}{{600}} \times 100\\
\Rightarrow \% {\rm{Marks obtained by Nancy }} = 71\%
\]

Now similarly,
Marks obtained by Rohit $ {x_2} = 560 $
Total marks available for Nancy $ {y_2} = 800 $
So, the percentage of the marks obtained by Rohit are given by-
\[
\Rightarrow \% {\rm{Marks obtained by Rohit = }}\dfrac{{{\text{Marks obtained by Rohit}}}}{{{\text{Total marks available for Rohit}}}} \times 100\\
\Rightarrow \% {\rm{Marks obtained by Rohit }} = \dfrac{{{x_2}}}{{{y_2}}} \times 100\\
\Rightarrow \% {\rm{Marks obtained by Rohit }} = \dfrac{{560}}{{800}} \times 100\\
\Rightarrow \% {\rm{Marks obtained by Rohit }} = 70\%
\]
 $ $
By comparing both the %Marks for Nancy and Rohit we see that the value of the %Marks of Nancy are greater than the %Marks of Rohit.
\[
\Rightarrow \% {\text{Marks obtained by Nancy}} > \% {\text{Marks obtained by Rohit}}\\
\Rightarrow 71\% > 70\%
\]
Therefore, the performance of Nancy is better than Rohit.

Note: It should be noted that we have used the percentage method because the value of the total marks for both Nancy and Rohit are different which means that in order to compare their performances, we have to find a common scale to compare. So, we find the percentage value of their marks obtained in this way we are comparing both of their marks on the scale of out of 100 percent. Now by using the percentage marks obtained we can easily compare their performances and find out whose performance is better.