Question

A science class has two times as many boys as girls. During the final examination of the year, the girls average 90 points each, and the class as a whole averages 80 points per person. What is the average score of the boys in the class?

Answer 1

Average score of boys is 75.

Explanation:

Let the number of boys in the class be = x

Let the number of girls in the class be = y

Since it is given that boys are twice in number than of girls thus we have

2y = x ......................(i)

By definition of average we have

`Average_(boys)=(\sum Marks_(boys))/(x)`

Similarly

`Average_(girls)=(\sum Marks_(girls))/(y)`

`Average_(class)=(\sum Marks_(boys)+\sum Marks_(girls))/(x+y).......(iii)`

Now it is given that average score of class is 80 points per person

Using this in the equation '3' we get

`80=(\sum Marks_(girls)+\sum Marks_(boys))/(x+y)\\\\Average_(class)=(\sum Marks_(girls))/(x+y) +(\sum Marks_(boys))/(x+y)\\\\80=(90y)/(3y)+(\sum Marks_(boys))/(x+(x)/(2))\\\\80=30+(\sum Marks_(boys))/((3x)/(2))\\\\50=(2)/(3)* (\sum Marks_(boys))/(x)\\\\\therefore Average_(boys)=(3)/(2)* 50=75`