Ans: D
Let $x\text{ cm}$ be the mean height of the $25$ teachers.
Let $x\text{ cm}$ be the mean height of the $25$ teachers.
$\begin{array}{rcl}
\dfrac{25\times x + 140 \times 145}{25+140} & = & 150 \\
25x + 20\ 300 & = & 24\ 750 \\
25x & = & 4\ 450 \\
x & = & 178
\end{array}$
Therefore, the mean height of the teachers is $178\text{ cm}$.