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Que: In a class, 80 percent of the boys and 20 percent of the girls play basketball. If ....

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Que: In a class, 80 percent of the boys and 20 percent of the girls play basketball. If ....

by Max@Math Revolution » Thu Jun 17, 2021 8:57 pm

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Que: In a class, 80 percent of the boys and 20 percent of the girls play basketball. If 75 percent of all the students play basketball, what is the ratio of the number of girls that did not play basketball to the number of boys who play basketball?

(A) \(\frac{2}{5}\)

(B) \(\frac{5}{2}\)

(C) \(\frac{1}{11}\)

(D) \(\frac{5}{11}\)

(E) \(\frac{13}{11}\)
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Re: Que: In a class, 80 percent of the boys and 20 percent of the girls play basketball. If ....

by Max@Math Revolution » Fri Jun 18, 2021 9:23 pm
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

=> 80 percent of the boys: \(\frac{60}{100}\)* 100b = 80b (Each)

=> 20 percent of the girls: \(\frac{20}{100}\) * 100g = 20g(Each)

=> 75 percent of all the students: \(\frac{75}{100}\) * 100(b + g) = 75(b + g) (Together)

Then, we get 80b + 20g = 75(b + g) = 75b + 75g.

Rearranging gives us that 80b – 75b = 75g – 20g

=> 5b = 55g, b = 11g.

Ratio of number of girls who did not play basketball : Ratio of number of boys who plays basketball:

=> 80g : 80b = g : b = g : 11g = 1 : 11

=> 1:11

Thus, the ratio of number of girls to the number of boys: 1:11

Therefore, C is the correct answer.

Answer C
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