Question

The average weight of all the students in a class is 58 kg, and that the average weight of all the 10 girls of the class is 50 kg. If the average weight of boys is 60 kg, how many students are there in the class?

A. 30
B. 40
C. 50
D. 60​

Answer 1

ans is C. 50

let average weights of boys in a class is x1 and number of boys is N1

& average weights of girls in a class is x2 and number of girls is N2

& the average weights of all students in a class is X1.2

given,

X1 =60 K. g. , X2 =50 K.g. , N1. = ? ,N2 = 10, X1.2= 58 K. g

X1.2 = X1 . N1 + X2. N2 /N1+N2

=> 58 = 60 .N1 +50 .10/N1 .10

=>58(N1+10) =60 N1+500

=>58N1+580= 60N1+500

=>60N1-58N1= 580-500

=>2N1 = 80

=>N1= 80/2

=>N1=40

hence the total number of students in a class is 50.

Answer 2

Answer:

The number of student in the class is 50.

Explanation:

Given: Average weight of all the students in the class is 58 kg

Average weight of all the 10 girls of the class is 50 kg.

Average weight of boys is 60 kg.

Find: Number of students are there in the class.

Solution:

We know that,

$Average=\frac{Sum of observation}{No. of observation}$

The average weight of 10 girls of the class =50 kg

So, the

$\frac{Sum of weight of 10girls}{10} =50\\Sum of weight of 10 girls =50\times 10$

Sum of weight of 10 girls = 500

Let $x$ represents the no of boys in the class.

Therefore,

The average weight of $x$ no of boys of the class = 60 kg.

i.e. $\frac{Sum of weight of x boys}{x} =60\\Sum of weight of x boys =60\times x$

The average weight of all the students in a class is 58 kg.

Therefore, we can form the equation as

$\frac{sum of weight of 10 girls + sum of weight of x boys}{10+x} =58\\\frac{500+60x}{10+x}=58\\ 500+60x=58(10+x)\\500+60x=580+58x\\60x-58x=580-500\\2x=80\\x=40$

So, the no of students in a class is 50.

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