Because resistors A, B and C are connected together in series, they all have the same current. Since the current through resistor C is 3A, the current through both of the resistors A and B are also 3A.
The three-resistor network containing resistors A, B and C is equivalent to the resistor on the left labeled ‘ABC’. The word ‘equivalent’ means that the voltage, current and resistance of resistor ABC are equal to the voltage, current and resistance of the three-resistor series network. In particular, the 3A that flows in one end and out of the other end of the three-resistor network must be the same as the current through resistor ABC. Thus the current through the equivalent resistor ABC is also 3A.
Resistors A and B are connected together in series. Together, they are equivalent to the single resistor on the left labeled ‘AB’. The word ‘equivalent’ means that the voltage, current and resistance of resistor AB are equal to the voltage, current and resistance of the two-resistor series network. In particular, the 5A of current through resistor AB must equal the current through resistor A as well as B. The currents through both resistors A and B are 5A.