Correct Answer - Option 2 : 23 : 28
Given:
Number of boys = 30
Number of girls = 20
Average marks of class = 25
Formula Used:
Average = Sum of marks/Number of students
Calculations:
Let the average marks of girls be x.
⇒ Average marks of boys = (x - 5)
Number of boys = 30
⇒ Total marks of boys = 30 × (x - 5) = (30x - 150) ----(1)
Number of girls = 20
⇒ Total marks of girls = 20 × x = 20x ------(2)
Average marks of class = 25
⇒ Total marks of class = 25 × (20 + 30) = 1250 ----(3)
Adding (1) and (2) and equating it with (3),
(30x - 150) + 20x = 1250
⇒ 50x = 1400
⇒ x = 28
Ratio of average marks of boys to that of girls = (x - 5)/x = (28 - 5)/28
⇒ Ratio of average marks of boys to that of girls = 23 : 28
∴ The ratio of average marks of boys to that of the girls is 23 : 28.