Question

In a co-ed school there are 15 more girls than boys. If the number of girls increased by 10% and the number of boys increased by 16%, there would be 9 more girls than boys. Find the number of students in school.

Answer 1

Hint: Here we have to find the number of students in school. That is the total number of boys and girls. So, we will proceed with two variables and two equations. In solving them we will get the number of girls and boys also.

Complete step-by-step answer:
Let the number of girls be x and number of boys be y.
From first statement
 x-y=15 ………. Equation 1
In second statement , number of girls are increased by 10%
x+10% of x = \[x + \dfrac{{10}}{{100}}x\]= \[1.1x\]
 And that of boys is increased by 16%
y + 16% of y = \[y + \dfrac{{16}}{{100}}y\]=1.16y
So from second statement
\[1.1x - 1.16y = 9\] ………..Equation 2
Now to solve equation 1 and 2, we have to multiply equation 1 by 1.16 then it becomes
\[1.16x - 1.16y = 17.4\] ………Equation 3
Now subtract equation 2 from equation 3.
\[1.16x - 1.16y - \left( {1.1x - 1.16y} \right) = 17.4 - 9\]
Multiply with minus sign in bracket
\[1.16x - 1.16y - 1.1x + 1.16y = 8.4\]
Now terms of y will get cancelled because they have the same coefficient with different signs .
\[1.16x - 1.1x = 8.4\]
You will get
\[
  0.06x = 8.4 \\
  x = \dfrac{{8.4}}{{0.06}} \\
  x = \dfrac{{840}}{6} \\
  x = 140 \\
\]
This is the number of girls in school.
Number of boys = x-15= 140-15= 125
Therefore total number of students= 140+125=265.

Note: When we come across problems with two variables like this ,you can go for constructing equations and solving them . But remember one thing if there are two variables then two separate conditions should be there to form equations.
Always remember ,when you either add or subtract an equation, the right hand side of one equation should be added or subtracted from the right hand side of the other equation . And same for the left hand side also.