The mean weight of 60 students in a class is 40 kg. The mean weight of boys is 50 kg while that of girls is 30 kg. Find the number of boys and girls in the class.

Given:

Mean weight of boys = 50

Mean weight of girls = 30

Let the number of boys and girls be a and b respectively.

Mean weight of boys = $\dfrac{\text{Sum of all weights of boys}}{\text{Number of all boys}}$

⇒ 50 = $\dfrac{\text{Sum of all weights of boys}}{a}$

⇒ Sum of all weights of boys = 50a

Mean weight of girls = $\dfrac{\text{Sum of all weights of girls}}{\text{Number of all girls}}$

⇒ 30 = $\dfrac{\text{Sum of all weights of girls}}{b}$

⇒ Sum of all weights of girls = 30b

Mean weight of 60 students = $\dfrac{\text{Sum of all weights of students}}{\text{Number of all students}}$

⇒ 40 = $\dfrac{50a + 30b}{a + b}$

⇒ 40(a + b) = 50a + 30b

⇒ 40a + 40b = 50a + 30b

⇒ 50a - 40a = 40b - 30b

⇒ 10a = 10b

⇒ a = b

Total students = 60

⇒ a + b = 60

⇒ a + a = 60

⇒ 2a = 60

⇒ a = $\dfrac{60}{2}$

⇒ a = 30

⇒ b = 30

Hence, the number of boys is 30 and the number of girls is 30.