The average marks (out of 100) of boys and girls in an examination are 75 and 80, respectively. If the average marks of all the students in that examination are 78. Find the ratio of the number of boys to the number of girls.

Options
a) 2 : 3
b) 1 : 2
c) 1 : 3
d) 3 : 4

Solution

As per question
Let assume no. of boys = x
No. of girls = y
Marks of boys = $ average marks \times no. of boys $
Marks of boys = $ 75 \times x = 75x $
Marks of girls = $ average marks \times no. of girls $
Marks of girls = $ 80 \times y = 80y $
Average marks of all student = $ \frac{marks of boys + marks of girls}{no. of boys + no. of girls}$
78 = $ \frac{75x + 80y}{x + y}$
75x + 80y = 78x + 78y
75x – 78x = 78y – 80y
3x = 2y
$ \frac{x}{y} = \frac{2}{3}$

Answer: a) 2 : 3