Question

The average score of boys in an examination of a school is 71 and that of girls is 73. The average score if school in examination 71.8. Find the ratio if number of boys to the number of girls that appeared in examination.

Answer 1

let the number of boys = x
number of girls = y
we need to find $\frac{x}{y}$.

The average score of boys in the examination is 71
total score of boys = 71 × x = 71x
The average score of girls in the examination is 73
total score of girls = 73 × y = 73y
So total mark of school = 71x + 73y     ---------------(1)

average score if school in examination 71.8
so total mark = 71.8 × (x+y)             -----------------(2)

From equations (1) and (2);
 
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

⇒$\frac{x}{y} = \frac{1.2}{0.8}= \frac{3}{2} =\boxed{3:2}$

Ratio of boys and girls is 3:2.

Answer 2

Answer: x:y::3:2

Step-by-step explanation:

To find- x:y

Let the total number of boys be x and total number of girls be y

Average score of 1 boy= 71

Total score of all boys= 71 × x

=71x

Average score of 1 girl= 73

Total score of all girls= 73 × y

= 73y

Total score of boys and girls= 71x + 73y _________(1)

Average score of all students = 71.8

Total number of students in the school = (x+y)

Total score of all students = 71.8 × (x+y) _________(2)

71x + 73y = 71.8x + 71.8y

73y - 71.8y = 71.8x - 71x

1.2y = 0.8x

x/y = 1.2/0.8

x/y = 3/2

x:y = 3:2