Question : In a school of 720 students, the ratio of boys to girls is 3 : 5. Find how many new boys may be allowed to the school if 18 new girls are admitted, so that the ratio of boys to girls changes to 2 : 3.
Option 1: 42
Option 2: 44
Option 3: 50
Option 4: 38
Correct Answer: 42
Solution :
In a school of 720 students, the ratio of boys to girls is 3 : 5.
⇒ Number of boys in the school $= 720 × \frac{3}{3+5} =720 × \frac{3}{8}= 270$
⇒ Number of girls in the school $= 720 × \frac{5}{3+5}=720 × \frac{5}{8}= 450$
Given that the number of new girls admitted to the school is 18.
Let $x$ be the number of new boys admitted to the school.
According to the question,
⇒ $\frac{(270+x)}{450+18}=\frac{2}{3}$
⇒ $3(270+x)=468×2$
⇒ $810+3x=936$
⇒ $3x=126$
$\therefore x=42$
Hence, the correct answer is 42.
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