Answer : Option A

Explanation :

average age of 36 students in a group is 14
$MF#%\text{=> Sum of the ages of 36 students = }36 \times 14
$MF#%
When teacher's age is included to it, the average increases by one => average = 15
$MF#%\begin{align}
&\text{=> Sum of the ages of 36 students and the teacher =}37 \times 15\\\\
&\text{Hence teachers age = }37 \times 15 - 36 \times 14 = 37 \times 15 - 14\left(37-1\right) = 37 \times 15 - 37 \times 14 + 14\\\\
&= 37 \left(15 - 14\right)+ 14 = 37 + 14 = 51
\end{align} $MF#%