Step 1:

Find the current through 100 resistor :

Super Position Theorem :

Take one voltage source at a time and replace all other with short or internal resistance.

Indicate the direction of current in the above circuit.

Equivalent resistance :

100 resistor is in parallel with 40 resistor.

Resistance R_T is in series with 60 resistor.

Step 2:

Circuit current :

Current across each resistor :

Step 3:

Now Short circuit the second voltage source.

Indicate the direction of current in the above circuit.

Equivalent resistance :

60 resistor is in parallel with 40 resistor.

Resistance R_T is in series with 100 resistor.

Step 4:

Circuit current :

Current across each resistor :

 Step 5:

Current through 100 resistor =

             = Current produced by 100 resistor due to 80 V - Current produced by 100 resistor due to 50 V

                   (Since they are in opposite direction)

             = 0.645 - 0.161

             = 0.484

Current through 100 resistor is 0.484 A.

 Step 6:

Power decipated at 100 :

Power decipated trough 100 resistor is 23.4 W.