The current gain $\beta$ may be defined as :

The input between the base and  emitter applies in a normal emitter or grounded emitter configuration, and the output is obtained between the collector and  emitter. This type of configuration is the most common circuit used in transistor-based amplifiers and is the usual way to connect bipolar transistors.  In a grounded-emitter amplifier circuit, the current flowing from the transistor must be equal to the current flowing through the transistor. Due to load resistance $\left(R_L\right)$the current gain of a typical emitter transistor configuration is very high due to the series collector ratio.$\frac{I_C}{I_B}$ 

Transistor current gain is given in beta  $\beta$.
The current gain $\beta$ is defined as the ratio of the change in collector current to the change in base current when the collector voltage of the grounded emitter circuit is constant. 

$\beta =\frac{∆i_C}{∆i_B}$
Or rewrite as.

 $\beta =\frac{I_C}{I_B}$
Next, slight fluctuations in the current flowing through the base regulate the current in the emitter-collector circuit. Generally, for general purpose transistors, the β value is 20-200. Therefore, if the beta value of the transistor is 100, for example, one electron is transferred to the base terminal for every 100 electrons flowing between the emitter and collector terminals. We then conclude that the current gain β is the ratio of the  change in collector current to the change in base current for a constant collector voltage in the grounded emitter circuit. Therefore, option B is correct.