Question

A class has x boys and y girls. In an exam, the average score for the boys is
63 and the average score for the girls is 70. The average for the whole class
is 68. Which of the following are possible values of x and y?

Answer 1

Average = (Total score)/No of scorers

x is the number of boys and their average is 63
So,
Total score of boys = 63x

y is the number of girls and their average is 70
So,
Total score of girls = 70y

Now,
The average for whole class is,
68
So,
(63x +70y)/(x + y) = 68
63x + 70y = 68x +68y
5x = 2y
x=(2/5)y
So,
The possible number of girls and boys is,
(5,2)
(10,4)
(15,6)
(20,8)
.
.
.

Answer 2

Given that the class has x boys and y girls.

Given,

Sum of scores of boys = 63x.

Sum of scores of girls = 70y.

The average score of all the students:

(63x + 70y)/(x + y) = 68

63x + 70y = 68( x + y)

63x + 70y = 68x + 68y

63x - 68x = 68y - 70

-5x = -2y

5x = 2y

(x/y) = 2/5.

Possible values of x and y :

(i) (4,10)

(ii) (6,15)

(iii) (8,20).

(iv) (10,25)



Hope it helps!