In an examination, the average marks obtained by 30 boys of the class is 5 less than the average marks obtained by 20 girls of the class. If the average marks of the whole class is 25, then find the ratio of average marks of boys to that of the girls.?

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.