Question

The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 72.25, find the ratio of the number of boys to the number of girls.

Answer 1

Let the number of boys and girls be x and y respectively.

Now,

Given, Mean marks of x boys in the examination = 70
⇒  Sum of marks of x boys in the examination = 70x

Given, Mean marks of y girls in the examination = 73
⇒  Sum of marks of y girls in the examination = 73y

Given, Mean marks of all students ( x + y ) in the examination = 72.25
⇒  Sum of marks of all students ( x + y ) students in examination = 72.25( x + y )

Now, the Sum of marks of all students ( x + y ) students in the examination
⇒  Sum of marks of x boys in the examination + Sum of marks of y girls in the examination

⇒ 72.25( x + y ) = 70x + 73y

⇒ 72.25x + 72.25y = 70x + 73y

⇒ 72.25x − 70x = 73y − 72.25y

⇒ 2.25x = 0.75y

⇒ `x/y = 0.75/2.25`

⇒ x : y = 1 : 3

Thus, the ratio of the number of boys to the number of girls is 1 : 3.