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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