2015-I-12

$\begin{array}{cl}
= & \dfrac{40 + 42 + \ldots + 79}{20} \\
= & 55 \text{ kg}
\end{array}$

The median

$\begin{array}{cl}
= & \dfrac{52 + 52}{2} \\
= & 52 \text{ kg}
\end{array}$

The range

$\begin{array}{cl}
= & 79 – 40 \\
= & 39\text{ kg}
\end{array}$

Suppose one of the new comers weighs $39\text{ kg}$. For the mean is increased by $1\text{ kg}$,

$\begin{array}{rcl}
\dfrac{1100 + 39 + x}{22} & = & 56 \\
x & = & 93
\end{array}$

However, the new range becomes $53\text{ kg}$, not $40\text{ kg}$. Hence, this case is rejected.

Suppose one of the new comers weighs $80\text{ kg}$. For the mean is increased by $1\text{ kg}$,

$\begin{array}{rcl}
\dfrac{1100 + 80 + x}{22} & = & 56 \\
x & = & 52
\end{array}$

Hence, the weights of the two students are $52\text{ kg}$ and $80\text{ kg}$.