Question

The mean weight of 60 students of a class is 52.75 kg. If the mean weight of 25 of them is 51 kg, find the mean weight of the remaining students.

Answer 1

Mean weight of 60 students of the class= 52.75 kg
Mean weight of 25 of them = 51 kg
Sum of the weights of those 25 students = $(25\times 51)\mathrm{kg}=1275\mathrm{kg}$
Now,
Let the sum of weights of the remaining 35 students be x kg.
Thus, we have:


$$\begin{gathered} \frac{\mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{weights}\mathrm{of}25\mathrm{students}+\mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{weights}\mathrm{of}\mathrm{the}\mathrm{remaining}35\mathrm{students}}{60}=\mathrm{Mean}\mathrm{weight}\mathrm{of}60\mathrm{students} \\ \Rightarrow \frac{1275+x}{60}=52.75 \\ \Rightarrow 1275+x=3165 \\ \Rightarrow x=1890 \\ \therefore \mathrm{Mean}\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{remaining}35\mathrm{students}=\frac{1890}{35}=54\mathrm{kg} \end{gathered}$$