Question

The average weight of $25$ students of grade $7$ is $40\text{kg}$. If the weight of teacher is included, then the average weight becomes $41.5\text{kg}$. Find the weight of the teacher.

• A. $81.5\text{kg}$
• B. $79\text{kg}$
• C. $43\text{kg}$

Answer 1

The correct option is B $79\text{kg}$

The formula to calculate the weighted average is,

$\text{Weighted Average}=\frac{(w_1\times n_1)+(w_2\times n_2)+\dots +(w_l\times n_l)}{w_1+w_2+\dots +w_l}$,

where $w_1,w_2,\dots w_l$ are the weighted factors and $n_1,n_2,\dots n_l$ are the data points.

Let the weight of the teacher be $x$ kg.

Here, the weighted factors are the number of students and the number of teachers, i.e., $w_1=25$ and $w_2=1$ and their corresponding average weight $n_1=40$ and $n_2=x$ are the data points.

It is given that the average weight of students and the teacher is $41.5$ kg.
Substitute the given values in the formula of weighted average to calculate the value of $x$.

$\begin{array}{cc}41.5& =\frac{(25\times 40)+(1\times x)}{25+1}\\ 41.5& =\frac{1000+x}{26}\\ 41.5\times 26& =1000+x\\ 1079& =1000+x\\ x& =1079-1000\\ x& =79\end{array}$

Hence, the weight of the teacher is $79\text{kg}$.

So, option (b) is correct.