Question

The mean weight of a class of 34 students is 46.5 kg. If the weight of the teacher is included, the mean rises by 500 gm. Then weight of the teacher is:
(a) 175 kg
(b) 62 kg
(c) 64 kg
(d) 72 kg

Answer 1

Hint: Firstly, we have to find the sum of the weights of 34 students from the given mean of weights of 34 students using the formula $\text{Mean}=\dfrac{\text{Sum of all the values}}{\text{Total number of values}}$ . Then, we have to add 500 g (after converting it to kilograms) with the given mean to get the mean of weights of 34 students and the teacher. Then, we have to use the formula of mean to get the value of the sum of weights of 34 students and the teacher. Finally, to find the weight of the teacher, we have to subtract the sum of weights of 34 students from the sum of weights of 34 students and teacher.

Complete step by step solution:
We are given that the mean weight of a class of 34 students is 46.5 kg. We know that mean is given by the formula
$\text{Mean}=\dfrac{\text{Sum of all the values}}{\text{Total number of values}}$
Therefore, we can find the total weight of the students using the above formula.
$\begin{align}
  & \Rightarrow \text{Mean}=\dfrac{\text{Sum of the weights of all the students}}{\text{Total number of students}} \\
 & \Rightarrow 46.5=\dfrac{\text{Sum of the weights of all the students}}{34} \\
\end{align}$
Let us move 34 from the RHS to the LHS.
$\begin{align}
  & \Rightarrow \text{Sum of the weights of all the students}=46.5\times 34 \\
 & \Rightarrow \text{Sum of the weights of all the students}=1581\text{ kg} \\
\end{align}$
We are given that if the weight of the teacher is included, the mean rises by 500 gm. Let us convert 500 gm to kg. We know that
$\begin{align}
  & \Rightarrow \text{1 kg}=1000\text{ g} \\
 & \Rightarrow \text{1 g}=\dfrac{1}{1000}\text{ kg} \\
\end{align}$
Therefore, we can convert 5000 gm to kilograms by multiplying the RHS of the above conversion by 500.
$\begin{align}
  & \Rightarrow 500g=\dfrac{500}{1000}\text{ kg} \\
 & \Rightarrow 500g=0.5\text{ kg} \\
\end{align}$
Therefore, we can find the mean weight of students and the teacher by adding 0.5 kg to 46.5 kg.
$\Rightarrow \text{Mean weight of 34 students and teacher}=46.5+0.5=47\text{ kg}$
Therefore, we can find the sum of weights of the students and the teacher using the formula of mean.
$\begin{align}
  & \Rightarrow \text{Mean weight of 34 students and teacher}=\dfrac{\text{sum of weights of the students and the teacher}}{\text{Total number of students and teacher}} \\
 & \Rightarrow \text{47}=\dfrac{\text{sum of weights of the students and the teacher}}{34+1} \\
 & \Rightarrow \text{47}=\dfrac{\text{sum of weights of the students and the teacher}}{35} \\
\end{align}$
Let us move 35 from the RHS to the LHS.
$\Rightarrow \text{sum of weights of the students and the teacher}=47\times 35=1645\text{ kg}$
Now, to find the weight of the teacher, we have to subtract the sum of weights of 34 students from the sum of weights of 34 students and teacher.
$\begin{align}
  & \Rightarrow \text{Weight of teacher}=\left( \text{Weight of 34 students}+\text{teacher} \right)-\text{Weight of 34 students} \\
 & \Rightarrow \text{Weight of teacher}=1645-1581 \\
 & \Rightarrow \text{Weight of teacher}=64\text{ kg} \\
\end{align}$
Hence, the correct option is C.

Note: Students must learn the formula of mean and how to find the sum of all values using it. They must make all the units constant, that is, they must convert 500 g to kg before doing any other operations. Students must never forget to write the units at the end of each calculation.