The mean of the age of three students Vijay, Rahul and Rakhi is 15 years. If their ages are in the ratio 4 : 5 : 6 respectively, then find their ages.

Let age of Vijay, Rahul and Rakhi be 4x, 5x and 6x respectively..

Mean age = $\dfrac{\text{Sum of age of students}}{\text{No. of students}}$

Sum of age of students = 4x + 5x + 6x = 15x.

$\therefore 15 = \dfrac{15x}{3} \\[1em] \Rightarrow 15 \times 3 = 15x \\[1em] \Rightarrow x = \dfrac{15 \times 3}{15} \\[1em] \Rightarrow x = 3.$

Vijay's age = 4x = 4 × 3 = 12 years,

Rahul's age = 5x = 5 × 3 = 15 years,

Rakhi's age = 6x = 6 × 3 = 18 years.

Hence, age of three students Vijay, Rahul and Rakhi are 12, 15 and 18 years respectively.