Where am I wrong about my calculation of power loss?
In both the methods the answer is 21.333
There is a mistake in the calculation of the first method because of 0.6 = 16k/x and not x/16k
Now coming to the solution
As far as I know, there is no direct formula linking power factor and power loss. Either there is something missing from the question or missing in the assumption.
If the power factor increases the True power of the system should increase and the apparent power should decrease and the loss depends on the circuit given.