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?​

Answer 1

Given:

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

To find:

How many students are there in the class?​

Solution:

We know,

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

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

i.e., $\frac{Sum \:of \:weight\:of \:10\:girls}{10} = 50$

$\implies Sum \:of \:weight\:of \:10\:girls = 50 \times 10$

$\implies Sum \:of \:weight\:of \:10\:girls = 500$

Let "n" represents the no. of boys in the class.

Therefore,

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

i.e., $\frac{Sum \:of \:weight\:of \:n\:boys}{n} = 60$

$\implies Sum \:of \:weight\:of \:n\:boys = 60 \times n$

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

Therefore, we can form the equation as,

$\frac{[Sum \:of \:weight\:of \:10\:girls] + [Sum \:of \:weight\:of \:n\:boys]}{10 + n} = 58$

$\implies \frac{[500] + [60n]}{10 + n} = 58$

$\implies 500+ 60n = 58(10 + n)$

$\implies 500+ 60n = 580 + 58n$

$\implies 60n - 58 n = 580 - 500$

$\implies 2 n =80$

$\implies \bold{n =40}$

∴ No. of students in the class = 10 + n = 10 + 40 = 50

Thus, there are 50 students in the class.

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