Question

The average score of boys in exams of school is 71 and that of girls is 73. The average score of the school is 71.8 . Find the ratio of no. of boys and no. of girls who appeared for the exam

Answer 1

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Number of boys be x

Number of girls be y

Average score of boys in exams = 71

Total score =71 × x = 71x

Average score of girls in exam = 73

Total score = 73 × y = 73y

Total marks obtained in school = 71x + 73y (i)

If the average score of school is 71.8

Total mark = 71.8 × (x+y) (ii)

From (i) and (ii) equation:

$71x + 73y = 71.8(x + y) \\ \\ = > 71x + 73y = 71.8x + 71.8y \\ \\ = > 73y - 71.8y = 71.8x - 71x \\ \\ = > 1.2y = 0.8x \\ \\ = > 0.8x = 1.2y \\ \\ = > \frac{x}{y} = \frac{1.2}{0.8} = \frac{3}{2} = 3:2$

Hence the ratio of boys and girls is 3:2

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