Question

If 60% of the students in a school are boys and the girl’s number is 812, how many boys are there?

Answer 1

Hint: For this problem we first let total numbers of students in a school be ‘x’. Then finding percentage of girls from boys percentage and then calculating respective percentage of girls with respect to total students and then equating the number of girls given in problem to an equation and then solving that equation to find value of ‘x’ and using it to find number of boys in a school.

Complete step-by-step answer:
Let total number of students in a school = x
Percentage of boys in a school is = $ 60\% $ .
Therefore, percentage of girls in a school will be given as: $ 100 - (percentage\,\,of\,\,boys) $
Percentage of girls = $ 100 - 60 = 40\% $
Total number of girls are in a school = $ 812 $ .
Therefore, from above we have,
 $
  40\% \left( x \right) = 812 \\
   \Rightarrow \dfrac{{40}}{{100}}\left( x \right) = 812 \\
   \Rightarrow x = 812 \times \dfrac{{100}}{{40}} \\
   \Rightarrow x = 203 \times 10 \\
  x= 2030 \;
  $
Hence, from above we see that total numbers of students in a school are = $ 2030 $
Also, percentage of boys in school is given = $ 60\% $
Therefore, we have
Number of boys in a school are = $ 60\% \,\,of\,\,\left( {total\,\,students\,\,in\,\,school} \right) $
 $
   \Rightarrow 60\% \left( {2030} \right) \\
   \Rightarrow \dfrac{{60}}{{100}} \times 2030 \\
   \Rightarrow 6 \times 203 \\
   \Rightarrow 1218 \;
  $
Hence, from above we see that the number of boys in school is $ 1218 $ .

Note: We can also find the solution of the problem in ratio form. In this we first find the ratio of percentage of boys and girls and then find ratio of number of boys (taking as ‘x’) and girls. Then equating both ratios to find the value of ‘x’ or required number of boys in a school.