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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?

Solution

✅ Correct Option: 3

Total students = 48

Ratio of boys to girls = 5:3

A ratio of 5:3 means for every 5 boys, there are 3 girls.

Boys = 5 parts

Girls = 3 parts

Total parts = 5 + 3 = 8 parts

Since total students = 48:

8 parts = 48 students

1 part = 48 ÷ 8 = 6 students

Therefore:

Boys = 5 × 6 = 30

Girls = 3 × 6 = 18


The new ratio needs to be 6:5 (boys to girls).

The number of boys stays the same = 30

Let xx be the number of girls to add.

New number of girls = 18 + xx

Number of boys = 30

The new ratio is:

30:(18+x)=6:530 : (18 + x) = 6 : 5


3018+x=65\dfrac{30}{18 + x} = \dfrac{6}{5}

30×5=6×(18+x)30 \times 5 = 6 \times (18 + x)

150=108+6x150 = 108 + 6x

42=6x42 = 6x

x=7x = 7


Therefore, 7 girls need to be added to the gathering.

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