Just to clarify for those who search this question up:

The key to this question is that △Y = △C + △S.

To illustrate how we get there:

We know that MPS = △S/△Y, and MPC = △C/△Y and that MPS + MPC = 1.

Combining these two things, that means that △C/△Y + △S/△Y = 1, and if we multiply both sides by △Y, we get:

△Y = △C + △S

Relating it to this question.

△Y = 100 + 100 = 200

From there we calculate MPC and multiplier

MPC = △C/△Y = 100/200 = 0.5

k = 1/(1-MPC) = 1/0.5 = 2