The average age of 125 students in a group is 16.2 years. 40%of the students are boys and the rest are girls. The average age of the boys is 20% more than the average age of the girls. What is the average age(in years) of the boys?

18

Total age of 125 students = 125 × 16.2 = 2025 years

40% = \(\frac{2}{5}\)

Ratio of number of boys to girls = 2 : 3

5R = 125 ⇒  1R = 25

So , Number of boys = 2 × 25 = 50

Number of girls = 125 - 50 = 75

Ratio of average age of boys to girls = 6 : 5

According to question ,

50 × 6a + 75×5a = 2025

675a = 2025

a = 3

So , Average age of boys = 6 × 3 = 18 years