Question

A boy got $ 60 $ out of $ 80 $ in Hindi, $ 75 $ out of $ 100 $ in English, and $ 65 $ out of $ 70 $ in Arithmetic. In which subject is his percentage of marks the best? Also, find his overall percentage.

Answer 1

Hint: To find the percentage we first calculate ratio of numbers. In the numerator of the ratio we write a number whose percentage is required and in denominator we write that number with respect to which percentage is required and then multiply the result by hundred. And, also in case of many numbers we first calculate the sum of the numbers and then divide it with the total of numbers from which they obtain and then multiply it with hundred.
To find the marks percentage,
\[{\text{Marks percentage = }}\dfrac{{Marks{\text{ }}obtained}}{{Total{\text{ m}}arks}} \cdot 100\% \].
To find the overall percentage,
\[{\text{Overall percentage = }}\dfrac{{Total{\text{ }}Marks{\text{ }}obtained}}{{Total{\text{ m}}arks}} \cdot 100\% \]

Complete step-by-step answer:
We first calculate the boy's percentage in each individual subject.
Marks obtained by boy in Hindi = $ 60 $ out of $ 80 $
Therefore, to calculate its percentage, we divide marks obtained in subject Hindi with total marks of subject Hindi.
\[
  \therefore \,\,Hindi's\,\,Percentage = \dfrac{{60}}{{80}} \times 100 \\
   \Rightarrow \,Hindi's\,\,Percentage = \dfrac{3}{4} \times 100 \\
   \Rightarrow \,Hindi's\,\,Percentage = 3 \times 25 \\
  \, \Rightarrow Hindi's\,\,Percentage = 75\% \\
 \]
Therefore, form above we see that his percentage in subject Hindi is $ 75\% $ .
Marks obtained by boy in English = $ 75 $ out of $ 100 $
Therefore, to calculate its percentage, we divide marks obtained in subject English with total marks of subject English.
\[
  \therefore \,\,English's\,\,Percentage = \dfrac{{75}}{{100}} \times 100 \\
   \Rightarrow \,English's\,\,Percentage = 75\% \\
 \]
Therefore, form above we see that his percentage in subject English is $ 75\% $ .
Marks obtained by boys in Arithmetic is $ 65 $ out of $ 70 $ .
Therefore, to calculate its percentage, we divide marks obtained in subject Arithmetic with total marks of subject Arithmetic.
\[
  \therefore \,\,Arithmetic's\,\,Percentage = \dfrac{{65}}{{70}} \times 100 \\
   \Rightarrow \,Arithmetic's\,\,Percentage = \dfrac{{13}}{{14}} \times 100 \\
   \Rightarrow \,Arithmetic's\,\,Percentage = 93\% \;
 \]
Therefore, form above we see that his percentage in subject Arithmetic is $ 93\% $ .
Hence, from above we see that percentage in three subjects Hindi, English and Arithmetic are $ 75\% ,\,\,75\% \,\,and\,\,93\% $ respectively.
Now, to calculate the total percentage of boys in all subjects.
For this we first calculate the sum of the marks obtained in all three papers. Which is given as,
 $ 60 + 75 + 65 = 200 $
Total of marks in all papers = $ 80 + 70 + 100 = 250 $
Hence, his percentage of marks = $ \dfrac{{total\,\,marks\,\,obtained\,\,in\,\,three\,\,papers}}{{sum\,\,of\,\,total\,\,marks\,\,in\,\,three\,\,papers}} \times 100 $
 $
   = \dfrac{{200}}{{250}} \times 100 \\
   = 20 \times 4 \\
   = 80\% \;
  $
Therefore, from above we see that boy got $ 80\% $ marks overall.

Note: To find percentage of marks students must take care one point that the sum of marks obtained will always be divided by total of marks in all subjects, but some time students divide sum of marks obtained by numbers of subjects, which is formula for mean but not for percentage and hence will get wrong answer of the problem.