Question

When 6 boys were admitted and 6 girls left, the percentage of boys increased from $$60\mathrm{\%}$$ to $$75\mathrm{\%}$$. Find the original number of boys and girls in the class.

Answer 1

Hint: According to the given question we are provided with some information about boys and girls in the class and we need to find the number of boys and girls using the given information. Also, we know that after the given condition the percentage of boys increased from $$60\mathrm{\%}$$ to $$75\mathrm{\%}$$.

Complete step by step answer:
According to the given question and information of the students we are being asked to find the number of girls and boys in the class. Now let us suppose that the number of boys is x and the number of girls is y. So, from this we get that the total students of the class are $x+y$ .
Now, we are given that initially boys percent was $$60\mathrm{\%}$$which can be written as ${\displaystyle \frac{x}{x+y}}={\displaystyle \frac{60}{100}}$ and when 6 boys were admitted and 6 girls left the percent becomes $$75\mathrm{\%}$$which can be written as ${\displaystyle \frac{x+6}{(x+6)+(y-6)}}={\displaystyle \frac{75}{100}}$ .
Now, simplifying first equation we get
 $\begin{array}{rl}& {\displaystyle \frac{x}{x+y}}={\displaystyle \frac{60}{100}}\\ & \Rightarrow 100x=60x+60y\\ & \Rightarrow 40x=60y\\ & \Rightarrow 2x=3y\end{array}$
And simplifying second equation we get
$\begin{array}{rl}& {\displaystyle \frac{x+6}{(x+6)+(y-6)}}={\displaystyle \frac{75}{100}}\\ & \Rightarrow 100x+600=75x+75y\\ & \Rightarrow 25x-75y=-600\\ & \Rightarrow x-3y=-24\end{array}$
Now, from the simplification of first equation we know that $2x=3y$ therefore using this in last equation we get
$\begin{array}{rl}& x-2x=-24\\ & \Rightarrow x=24\end{array}$
And putting this in the first equation we get $y=16$ .
Therefore, the numbers of boys and girls in the class are 24 and 16 respectively.

Note: Now, in this question we need to know how to form the problem mathematically after reading the question and then we should know how to evaluate the fractional algebraic equation and simplify it first. Also, we need to be aware of the various methods to solve equations.