Problem Solving

Que: In a class, 65 percent of the boys and 78 percent of the girls play basketball. If 72 percent of all the students play basketball, what is the ratio of the number of girls to the number of boys?

(A) \(\frac{4}{3}\)

(B) \(\frac{7}{6}\)

(C) \(\frac{8}{7}\)

(D) \(\frac{9}{8}\)

(E) \(\frac{13}{11}\)

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