Question

The total number of boys and girls in a class is 50. The average age of all the boys is 20 years, and the average age of all the girls is 15 years. If the total number of boys is 6 more than the total number of girls, find the average age (in years) of the whole class.
1. 16.5
2. 18.2
3. 17.4
4. 18.5
5. 17.8

Answer 1

Correct Answer - Option 5 : 17.8

Given:

Total number of boys and girls in the class = 50

The average age of all the boys = 20 years

The average age of all the girls = 15 years

Total number of boys = Total number of girls + 6

Formula Used:

Average age of a group of people  = Sum of age of all the people in the group/Total number of people in the group

Calculation:

Let the total number of girls in the class be x

So, the total number of boys in the class is (x + 6)

Hence, we get: 

x + (x + 6) = 50

⇒ x = 22

So, the total number of girls in the class = 22, and 

The total number of boys in the class = 22 + 6 = 28

So, we obtain the total age of all the boys and girls in the class = (28 × 20) + (22 × 15) = 890

The average age of all the 50 students in the class = 890/50 = 17.8 years

∴ The average age of the whole class is 17.8 years