Question

In a class, there are $35$ girls and $20$ boys and the total average weight of the class is $38\mathrm{kg}$. Total average weight of boys is $52\mathrm{kg}$. Find the approximate average weight of girls?

Answer 1

Step $1:$Find the total weight of the class and the total weight of all the boys.

Since, the average weight of the class is $38kg$ and the total number of students are $55$.

We know that the relation between the average weight is given by: $W_{av}=\frac{W}{n}$.

Where, $W$ is the total weight and $W_{av}$ is the average weight and $n$ is the number of persons whose average weight is to be calculated.

Therefore, the total weight $W$ of the class is given by:

$$\begin{gathered} W=55\times 38 \\ \Rightarrow W=2090 \end{gathered}$$

So, the total weight of the class is $2090kg$.

Since, the average weight of the boys is $52kg$ and there are $20$ boys in the class.

Therefore, the total weight $w_B$ of the boys is given by:

$$\begin{gathered} w_B=52\times 20 \\ \Rightarrow w_B=1040 \end{gathered}$$

So, the total weight of the boys is $1040kg$.

Step $2:$ Find the average weight of girls.

Since, the total weight $w_G$ of the girls is given by:

$$\begin{gathered} w_G=W-w_B \\ \Rightarrow w_G=2090-1040 \\ \Rightarrow w_G=1050 \end{gathered}$$

Since, the total weight of the girls is $1050kg$ and there are $35$ girls.

So, the average weight of the girls is $\frac{1050}{35}=30$.

Hence, the average weight of girls is $30kg$.