Question

In a class of 50 students, the average age of girls is 12.3 years and that of boys is 12.5 years. If the average age of the class is 12.42 years, then the number of boys and girls respectively in the class are

Answer 1

Solution :
let no of boys be X
so no of girls will be 50-X

sum of ages of boys = 12.5(X)
sum of ages of girls = 12.3(50-X) = 615 - 12.3(X)

avg age of class = {12.5(X) + 615 - 12.3(X)}/50 = 12.42
so,
0.2X + 615 = 621
0.2X = 6
X = 30
so no of boys = 30
no of girls = 50 - 30 = 20

hope that helps.!!!

Answer 2

Given : In a class of 50 students, the average age of girls is 12.3 years and that of boys is 12.5 years. If the average age of the class is 12.42 years.

To find : Number of boys and girls.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of boys and girls)

Let, the number of boys = x

So, the number of girls :

= Total students - Number of boys

= (50 - x)

Average age of boys = 12.5 years

Sum of the ages of the boys :

= Average age of boys × Number of boys

= (12.5 × x) years

= 12.5x years

Average age of girls = 12.3 years

Sum of the ages of the girls :

= Average age of girls × Number of girls

= [12.3 × (50 - x)] years

= (615 - 12.3x) years

Sum of the ages of the total students :

= Sum of the ages of the boys + Sum of the ages of the girls

= [(12.5x) + (615 - 12.3x)] years

= (615 + 0.2x) years

Now,

Total number of students = 50

Average age of the class = 12.42 years

So,

The sum of the ages of the total students :

= Average age of the class × Total number of students

= (12.42 × 50) years

= 621 years

Comparing the two values of the sum of the ages of the totals students,

615 + 0.2x = 621

0.2x = 621 - 615

0.2x = 6

x = 6/0.2

x = 30

So, the number of boys = x = 30

And, the number of girls = (50-x) = (50-30) = 20

Hence, there are 30 boys and 20 girls in the class.