Question

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

Answer 1

Let the no. of boys = x
 no. of girls = 60-x

A/Q,
 mean weight of boys = 50 kg
     Total weight  of boys ÷ x = 50 
⇒ total weight of boys = 50x
 
And,
mean weight of girls = 30 kg
    Total weight  of girls ÷ (60-x) = 30 
⇒  Total weight of girls = 30(60-x) =1800 - 30x
now,
mean weight of 60 students = 40 kg
     (Weight of girls + Weight of boys) ÷  total no. of students = 40
⇒   (1800 -30x + 50x) ÷ 60 =40
⇒   1800 + 20x =40 ×60
⇒    20x = 2400 - 1800
⇒    20x = 600
           x = 600/20 = 30
Therefore total no. of boys = 30
and total no of girls = 60 - 30 = 30
Therefore,
No. of Boys =30
No. of Girls = 30

Answer 2

Answer:

x = the number of girls

y = the number of boys

x + y = 60 ------------------------- equation (1)

Total weight of the students = 60(number of students)*40(their average weight) = 2400

Total weight of girls = x(the number of girls)*30(average weight of girls) = 30x

Total weight of boys = y(the number of boys)*50(average weight of boys) = 50x

Total weight of all students = Total weight of girls + Total weight of boys = 30x + 50y = 2400 ----- equation (2)

Solve equation 1 for either x or y and substitute the result in equation 1.

y=60-x

=> 30x + 50(60-x) = 2400

<=> 30x - 50x + 3000 = 2400

<=> -20x = -600

x = 30

=> y = 30

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