Ok, first of all, the expression you're using for the multiplier is only true in an economy with no government (and so no taxes) and no foreign trade. The more general formula is:
k = 1 / (marginal propensity to withdraw)
and the three withdrawals are savings, taxes and imports.
This is the same as:
k = 1 / (1 - mpc'')
where mpc'' is the marginal propensity to consume domestic goods out of national income.
Using the first method to answer this question:
The marginal propensity to tax is 0.4.
The marginal propensity to save is a bit more complicated as we have been given the mpc out of disposable income, whereas we want it out of national income. The mps out of disposable income is 1 - mpc, ie 0.3. To get the mps out of national income (mps'), we need to allow for tax. So mps' is 0.3 x (1 - 0.4) = 0.18.
So the multiplier is:
k = 1 / (0.18 + 0.4) = 1.72.
The injection (in this case an investment) was 120, so national income will go up by 120 x 1.72 = 207.
In questions like this, we assume that the economy was in equilibrium before the injection, and that it will be in equilibrium afterwards too (eventually anyway). Equilibrium occurs when national income and aggregate demand are equal, so aggregate demand will also increase by 207.
Aggregate demand is the sum of C, I, G, X and -Z. Here we have I going up by 120. However, C and Z are almost always dependent on national income, and since national income has increased, these will also increase. Since we don't know an actual value for national income, I don't think we can work out how much they will increase in this case, so we have to use the reasoning above!
