The mean weight of 150 students in a certain class is 60 kgms. The mean weight of boys in the class is 70 kgms and the girls is 55 kgms. Find the number of boys and the number of girls in the class
Answers
Answer:
100,50
Explanation:
Total students in class =150
mean weight=60kg
total weight =150×60=9000kg
Let the total number of boys =x
mean weight of boys =70kg
total weight of boys =70×x=70xkg
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=
15
75
x=0
So number of boys =50
number of girls =150−50=100
Answer:
We have
X₁ = Mean weight of boy = 70 kgs.
X2 = Mean weight of girl = 55 kgs.
X = Mean weight of all students = 60 kgs.
X = n₁X₁ +nX₂/n₁ + n₂
60 = n₁ × 70+ n₂ × 55/n₁ + n₂
60(n₁ + n₂) = 70n₁ + 55n2
60n₁ + 60n2 = 70n₁ + 55n2
10n₁ = 5n2
2n₁ = n₂ ...(ii)
Putting n₂ = 2n₁ from (ii) in (i), we get
n₁ + 2n₁ = 150
3n₁ = 150
n₁ = 50.
Putting n₁ = 50 in n₂ = 2n₁ , we get
n₂ = 100.
Hence, there are 50 boys and 100 girls in
the class.