Question

The mean weight of a class of 36 students is 41 kg. If one of the students leaves the class then the mean is decreased by 200 g. Find the weight of the student who left.

Answer 1

Mean weight of 36 students = 41 kg
Sum of the weights of 36 students = $\left(41\times 36\right)\mathrm{kg}=1476\mathrm{kg}$
Decrease in the mean when one of the students left the class = 200 g = 0.2 kg
Mean weight of 35 students = (41 $-$ 0.2) kg = 40.8 kg
Now,
Let the weight of the student who left the class be x kg.

$$\begin{gathered} \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \frac{\mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{weights}\mathrm{of}36\mathrm{students}-x}{35}=40.8 \\ \Rightarrow \frac{1476-x}{35}=40.8 \\ \Rightarrow 1476-x=1428 \\ \Rightarrow x=48 \end{gathered}$$

Hence, the weight of the student who left the class is 48 kg.