School A has boys to girls in the ratio 5 : 6 and school B has girls to boys in the ratio 8:7. If th

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20 Jun 2022 Ratio & Proportion

School A has boys to girls in the ratio 5 : 6 and school B has girls to boys in the ratio 8:7. If the number of students in school A is at least twice as many as the number of students in school B, what is the minimum percentage of boys when both schools are considered together?

OPtion

1) 37.5%
2) 33.33%
3) 39.17%
4) 34.39%
5) 48.32%
6) 45.86%
7) 48.08%
8) 54.17%
9) 36.06%
10) None of these

Solution

Let school A has Boys=5x, Girls=6x and school B has Boys=7y, Girls=8y
Given, number of students in school A is at least twice as many as the number of students in school B and we have to find minimum percentage of boys out of total students.
For the minimum percentage, we need to consider the other extreme-where school A has exactly twice as many students as school B.
⇒ (5x + 6x) = 2*(7y + 8y)
y=(11/30)*x
Now total boys=5x+7y=5x+7*(11/30)*x=(227/30)*x
Total students of school A & B = 11x+15y = 11x + 15*(11/30)*x = (33/2)*x
.'. Minimum percentage of boys = [(227/30)*x / (33/2)*x]*100 = 45.86%

Correct Option: 6 Best Solution (0)