Question about current?

Since C and D are open circuit, when 100 v is applied to AB, there is no current passing through the two 60-ohm resistors. Hence, there is also no potential drop across these two resistors

Because voltage across CD is 80 v, that indicates the voltage across R is 80 v. From A to B, current flows through the three resistors, 10-ohm, R, and 10-ohm connected in series. Therefore, voltage across the two 10-ohm resistors is (100 - 80) v = 20 v. That is, voltage across each 10-ohm resistor is 10 v.

Current through the 10-ohm resistor = 10/10 A = 1 A (Ohm's Law)
Thus, R = 80/1 ohms = 80 ohms.

Now, when 100 v is applied across CD, current flows through the 60-ohm resistor, R (= 80 ohms), and the other 60-ohm resistor.
Current = 100/(60 + 80 + 60) A = 0.5 A (Ohm's Law)

Because there no current flows through the two 10-ohm resistors and hence no potential drop across them, the voltage across R equals to the voltage across AB.

Voltage across R = 100 x [80/(60 + 80 + 60)] v = 40 v
Hence, voltage across AB = 40 v