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