Question : In a college union, there are 48 students. The ratio of the number of boys to the number of girls is 5 : 3. What is the number of girls to be added to the union so that the ratio of boys to girls is 6 : 5?
Option 1: 6
Option 2: 7
Option 3: 12
Option 4: 17
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Correct Answer: 7
Solution :
Given: Total number of students = 48
The ratio of the number of boys to the number of girls = 5 : 3
Number of boys = $\frac{5}{8}×48=30$
Number of girls = $\frac{3}{8}×48=18$
Let the $x$ number of girls to be added.
Then, according to the given conditions:
$\frac{30}{(18+x)}=\frac{6}{5}$
⇒ $30×5=6×(18+x)$
⇒ $150=108+6x$
⇒ $6x=42$
$\therefore x=7$
Hence, the correct answer is 7.
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