There are 100 students in a class. Number of boys is 10 more than the number of girls. The average weight of boys is 50 kg and average weight of the whole class is 45.5 kg. The average weight of girls is (in kg)
Answers
Let "number of boys" be denoted by A.
Let "number of girls" be denoted by B.
There are 100 students in a class.
- So total is written as A + B = 100
Given :- Number of boys is 10 more than the number of girls.
Number of boys = 10 + Number of girls
A = 10 + B
- A - B = 10
Let us add above two equations,
A + B = 100
A - B = 10
------------------------------------
2*A + 0 = 110
Therefore 2*A = 110
A = 110 / 2 = 55
number of boys = A = 55
A + B = 100 (plug A = 55 in this equation)
55 + B = 100
B = 100 - 55 = 45
number of girls = B = 45
The average weight of boys is 50 kg
x̅ = ∑Xi / n
50 = ∑Xi / 55
∑Xi = 2750 (Total weight of all 55 boys)
The average weight of the whole class is 45.5 kg
x̅ = ∑Xi / n
45.5 = ∑Xi / 100
∑Xi = 4550 ( Total weight of all 100 students in class)
Total weight of the whole class = Total weight of boys + Total weight of girls
4550 = 2750 + Total weight of girls
Total weight of girls = 4550 - 2750 = 1800
Let us use the formula of average ,
x̅ = ∑Xi / n
= 1800 / 45 = 40 Kg
The average weight of 45 girls from the class is 40 Kg