Question

The mean weight of 150 students in a class is 60 kg. The mean of boys in the class is 70 kg and that of girls is 55 kg. Find the number of boys and girls in the class.Solve it by using combined mean formula.​

Answer 1

Answer:

Total number of students = 150

Let the number of boys and girls be x and y respectively.

Then, x+y=150 ....(1)

Mean weight of x boys = 70 kg

→ Total weight of x boys = 70x kg.

Mean weight of y boys = 55 kg

→ Total weight of y boys = 55y kg

Mean weight of 150 students = 60 kg

→ Total weight of 150 students = 60 x 150 = 9000 kg

.. 70x + 55y = 9000

→ 14x+11y = 1800 ....(2)

Multiplying equation (1) by 11, we get

11x +11y 1650 ....(3)

Subtracting equation (3) from (2), we have

3x = 150

⇒x=50

Substituting x = 50 in (1), we get

50+ y = 150

⇒y=150-50 = 100

Hence, number of boys 50 and number of girls = 100.