Question

When $6$ new boys were admitted and $6$ girls left from the class, the percentage of girls decrased from $68$ to $56$. Find the original number of boys and girls in the class.

• A. Number of boys $=14$
  Number of girls$=32$
• B. Number of boys $=12$
  Number of girls$=30$
• C. Number of boys $=18$
  Number of girls$=36$
• D. Number of boys $=16$
  Number of girls$=34$

Answer 1

The correct option is D Number of boys $=16$

Number of girls$=34$
Let the original numberof boys and girls in the class be $x$ and $y$ respectively.
$\therefore$ Total number of students $x+y$
Now percentage of girls in the class is $68$ in the begining.

$\Rightarrow \frac{y}{x+y}=\frac{68}{100}$

$\Rightarrow \frac{y}{x+y}=\frac{17}{25}$

$\Rightarrow 25y=17x+17y\Rightarrow 17x-8y=\mathrm{0...}\left(i\right)$
Again, when $6$ boys were admitted and $6$ girls left, the number of students remained the same but the number of girls decreased to $y-6$ and percentage became $56$

$\frac{y-6}{x+y}=\frac{56}{100}$

$\Rightarrow \frac{y-6}{x+y}=\frac{14}{25}$

$\Rightarrow 25y-150=14x+14y$
$\Rightarrow 11y-14x=\mathrm{150...}\left(ii\right)$
Solving (i) and (ii), we get
$x=16,y=34$
Hence, number of boys $=16$
Number of girls $=34$