Question

the mean weight of 150 students In a class is 60 kg the mean weight of boys is 70 kg while that of girls is 55 kg. find the number of boys and girls.

Answer 1

total students in class = 150
mean weight = 60 kg
total weight = 150×60 = 9000 kg

Let the total number of boys = x
mean weight of boys = 70kg
total weight of boys = 70×x = 70x kg

total number of girls = total students - no. of boys = 150 - x
mean weight of girls= 55kg
total weight of girls = 55×(150-x) = 55×150 - 55x = (8250 - 55x) kg

Total weight = weight of boys + weight of girls
⇒ 9000 = 70x + (8250 - 55x)
⇒ 9000 = 70x + 8250 - 55x
⇒ 9000 - 8250 = 70x - 55x
⇒ 750 = 15x
⇒ x = 750/15 
⇒ x = 50

So number of boys = 50
number of girls = 150 - 50 = 100

Answer 2

Total no. of students=150
Let the no. of boys and girls be x and y
since, x+y =150------------(1)
Mean weight of X boys =70kg
therefore =70x kg
Mean weight of y girls =55kg
therefore=55y kg
Mean weight of 150 students = 60kg
total weight of 150 students =60×150=9000kg
therefore 70x+55y=9000
divided by 5
14x+11y=1800--------------(2)
in (1) multiply by 11
11x+11y=1650
14x+11y=1800
-. -. -
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3x=150
x=50
put in (1) x=50
50+y=150
y=100
therefore the no. of boys is 50 and no. of girls is
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