Question

After 10 girls joined a class, the ratio of the number of boys and girls becomes 11:14 from 11:9. The number of students in the class now is .

• A. 40
• B. 50
• C. 60
• D. 70

Answer 1

The correct option is B 50

Original ratio = $11:9$.
Therefore original number of boys and girls is $11x$ and $9x$ respectively.

Since 10 girls join the class the number of girls becomes $9x+10$

According to the given data,
$\frac{11x}{9x+10}=\frac{11}{14}$.

On solving the equation, we get
$\Rightarrow 11x\times 14=11\times (9x+10)\Rightarrow 154x=99x+110\Rightarrow 154x-99x=110\Rightarrow 55x=110\Rightarrow x=\frac{110}{55}\Rightarrow x=2$

Hence, the present number of boys is $11x=11\times 2=22$ and the number of girls is $9x+10=9\times 2+10=28$.

Therefore, the total number of students is $22+28=50.$