Que: In a class, 65 percent of the boys and 78 percent of the girls play basketball. If 72 percent of all ....

Solution: Let the number of the boys be 100b and the number of girls is 100g, then we get the total number of students to be 100(b+g).

As we are dealing with percent, according to the IVY approach take ‘100’ as total, and b and g are the initials of the words ‘boys’ and “girls” respectively.

Also, this question is applied by the IVY Approach, Each Each Together

=> 65 percent of the boys: \(\frac{65}{100}\) * 100b = 65b (Each)

=> 78 percent of the girls: \(\frac{78}{100}\) * 100g = 78g (Each)

=> 72 percent of all the students: \(\frac{72}{100}\) * 100(b+g) = 72(b+g) (Together)

Then, we get 65b + 78g = 72(b+g) = 72b + 72g.

Rearranging gives us 78g - 72g = 72b - 65b, 6g = 7b or g =\(\frac{7b}{6}\).

Ratio of number of girls : Ratio of number of boys:

=> 100g : 100b = g : b = \(\frac{7b}{6}\) : b = \(\frac{7}{6}\) : 1

=> 7 : 6

Thus, the ratio of number of girls to the number of boys: 7:6

Therefore, B is the correct answer.

Answer B