Question : The ratio of the number of boys to the number of girls in a class is 2 : 5. If 10 boys leave the class and 20 new girls join the class, then the new ratio of boys and girls in the class becomes 4 : 25. What is the number of boys in the class now?
Option 1: 12
Option 2: 8
Option 3: 9
Option 4: 22
Correct Answer: 12
Solution :
Given,
The ratio of the number of boys to the number of girls in a class is 2 : 5.
If 10 boys leave the class and 20 new girls join the class, then the new ratio of boys and girls in the class becomes 4 : 25
Let the number of boys in the class before be $2x$.
So, the number of girls in the class at that time is $5x$.
According to the question,
$\frac{2x−10}{5x+20}=\frac{4}{25}$
⇒ $50x - 250 = 20x + 80$
⇒ $30x = 330$
⇒ $x = 11$
Number of boys in class earlier = 2 × 11 = 22
⇒ The number of boys in the class now is 22 – 10 = 12
Hence, the correct answer is 12.
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