Answer
See the detailed answer below.
Work Step by Step
Let's assume that the dashed circle in the figures below is a Gaussian surface.
The positive charge in the cavity will pull the free electrons inside the neutral conductor toward it, as we see in the first figure below.
The net charge inside this Gaussian surface is then zero since the electrons pulled toward the positive charge are creating the same charge magnitude.
This means that the outer surface of the conductor will be positively charged by the same amount of +100 nC since the inner surface of the conductor is charged by -100 nC.
Now after adding the -50 nC charge to the conductor, the outer surface of the conductor will be affected by that and will have a net charge of +50 nC while the inner walls net charge remains -100 nC.
$$\color{blue}{\bf [a]}$$
$$Q_{inner}=\color{red}{\bf -100}\;\rm nC$$
$$\color{blue}{\bf [b]}$$
$$Q_{outer}=\color{red}{\bf +50}\;\rm nC$$
