An electricity and magnetism problem by Rishabh Deep Singh

This is a cool problem. It relies heavily on complex power analysis principles, the full scope of which is too large to cover here. The biggest things to consider are the following:

1) The complex power (active power (P) + j * reactive power (Q)) through a load, as a function of the voltage and current through it is:

$\vec{S} = P + jQ = \vec{V} \vec{I}^*$

Where $\vec{I}^*$ is the complex conjugate of $\vec{I}$

2) A load with leading power factor (capacitive) behaves as a reactive power source, and thus it consumes negative reactive power.

3) A load with lagging power factor (inductive) behaves as a reactive power sink, and thus it consumes positive reactive power.

Here is a sketch of my solution (programmed in Mathcad). I think the problem should state more clearly that it is looking for the RMS magnitude of the source voltage, truncated to the nearest integer (which turns out to be 123). @Rishabh Deep Singh , can you make this more clear?