There are 48 students in a college gathering. The ratio of the number of boys to the number of girls in the gathering is 5 : 3. If the ratio of the boys to girls has to be made 6 : 5, then how many girls need to be added to the gathering, without changing the numbers of boys who are attending the gathering?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7
Given:
- Total students = 48
- Ratio of boys : girls = 5 : 3
Step 1: Find number of boys and girls initially
Total ratio parts = 5 + 3 = 8
Each part = 48 ÷ 8 = 6
- Boys = 5 × 6 = 30
- Girls = 3 × 6 = 18
Step 2: New ratio required = 6 : 5
Number of boys remains 30
So,
$\frac{30}{\text{New girls}} = \frac{6}{5}$
$\text{New girls} = \frac{30 × 5}{6} = 25$
Step 3: Girls to be added
$25 - 18 = 7$