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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