the weight of 200 students in a class is 50 kg if the mean weight of boy in a class is 60 and that of girl is 44kg find the no. of boys and girls in the class
Answers
Answer:
No. of boys = 75
No. of girls = 125
Step-by-step explanation:
Let "x" = number of boys
Let "y" = number of girls
No. of boys + girls = 200 => x + y = 200
Mean weight of boys = 60 kg
Mean weight of boys = (Total weight of boys)/(No. of boys)
Total weight of boys = Mean weight of boys * No. of boys
= 60 * x .........Eqn 1
Similarly
Mean weight of girls = 44 kg
Mean weight of girls = (Total weight of girls)/(No. of girls)
Total weight of girls = Mean weight of girls * No. of girls
= 44 * y .........Eqn 2
We are given that mean weight of the class is 50 kg
=> Total weight of boys and girls / No. of boys and girls = 50
=> Total weight of boys and girls / 200 = 50
Using Eqn1 and Eqn2, we get:
(60x + 44y) / 200 = 50
60x + 44y = 10000 ......Eqn 3
Now, x + y = 200 => y = (200 - x)
Substituting for y in Eqn 3, we get:
60x + 44(200 - x) = 10000
60x + 8800 - 44x = 10000
16x = 10000 - 8800
16x = 1200
x = 1200 / 16
x = 75
y = 200 - x = 125
No. of boys = 75
No. of girls = 125
Verify:
Sum = No. of observations * Mean
Therefore,
Sum of weight of boys = 75*60 = 4500
Sum of weight of girls = 125*44 = 5500
Sum of weight of boys and girls = 4500 + 5500 = 10000
Total number of boys and girls = 75+125 = 200
Mean weight of boys and girls = 10000/200 = 50 (As given)
HOPE THIS WILL BE HELP YOU............
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