In an n-p-n common emitter (CE) transistor the collector current...

The change in collector current for the given transistor can be written as

$\begin{cases}∆ {I}_{c} & = & 16mA - 5mA \\ & = & 11mA\end{cases}$

The change in base current for the given transistor can be written as

$\begin{cases}∆ {I}_{b} & = & 200\muA - 100\muA \\ & = & 100\muA\end{cases}$

The formula to calculate the current gain in CE configuration is given by

$\beta = \dfrac{∆ {I}_{c}}{∆ {I}_{b}} . . . \left(1\right)$

Substitute the values of the known parameters into equation (1) to calculate the required quantity.

$\begin{cases}\beta & = & \dfrac{∆ {I}_{c}}{∆ {I}_{b}} \\ = & \dfrac{11mA}{100\mu A} \\ = & 110\end{cases}$