In a group of $7$ people, the average age is found to be $17$ years.
$\dfrac{x_{1} + x_{2} + \dots + x_{7}}{7} = 17$
$\implies x_{1} + x_{2} + \dots + x_{7} = 119 \rightarrow(1)$
Two more people joined with an average age $19$ years.
$\dfrac{x_{8} + x_{9}}{2} = 19$
$\implies x_{8} + x_{9} = 38\rightarrow(2)$
Now, $x_{1} + x_{2} + \dots + x_{7} + x_{8} + x_{9} = 119 + 38 = 157$
One person left the group whose age was $25$ years.
Lets $x_{9}$ leave the group. So $x_{9} = 25$
$x_{1} + x_{2} + \dots + x_{7} + x_{8} = 157 – 25 = 132$
Average $ = \dfrac{x_{1} + x_{2} + \dots + x_{7} + x_{8}}{8} = \dfrac{132}{8} = 16.5$ years.
So, the correct answer is $(B).$