Question

There are 30 students in a class whose average age is 20 years. The average age of the boys in the class is 3 less than the average age of the girls in it. If the age of their class teacher, which is between 49 years and 54 years is included with boys, the average age of the boys equals to that of the girls. If the average age of boys as well as the average age of girls are integers, then how many boys are there in the class?

• A. 11
• B. 12
• C. 10
• D. cannot be determined.

Answer 1

The correct option is C

10

The total of ages of the students of the class = 600 years.Let the number of boys in the class be x.Let there average be y.Let the age of teacher be z.
xy+(30-x)(y+3)=600
30y+90-3x=600 ; x=10y-170.
When teacher is also included $\frac{xy+z}{x+1}=y+3$
xy+z=xy+3x+y+3.
$z=\frac{x+170}{10}+3x+3=\frac{31x}{10}+20;$
Now use answer options.Only possibility is x=10.Option (c).