The average age of 120 students in a group is 13.56 years. 35% of the number of students are girls and the rest are boys. If the ratio of the average age of boys and girls is 6 : 5, then what is the average age (in years)of the girls?

Total students = 120

Number of girls = 120$$ \times \frac{35}{100}$$ = 42

Number of boys = 120 - 42 = 78

Total age of 120 student = 13.56$$\times 120$$ = 1627.2

Let the average age of boys and girls be 6x and 5x.

Total age of all girls = 42 $$\times$$ 5x = 210x

Total age of all boys = 78 $$\times$$ 6x = 468x

Total age of 120 student = total age of all girls + total age of all boys

1627.2 = 210x + 468x

x = 2.4

Average age of girls = 5x = 5$$\times$$ 2.4 = 12