Top Score has a different solution for this. They basically say that you know you end up with 40mL after the initial neutralization, and you know you have to add x amount of 1M HCl in order to arrive at a final concentration of .01M and a final volume of 40+x(amount that you added), so we get
1M(x)=(.01M)(40+x). You solve for x, which is about .4mL. You then take the total volume, which is 40.4mL, and substract 20mL from it because you aren't interested in NaOH. I could not follow the reasoning of this problem at all honestly. I was grateful there wasn't a question like this on my DAT.
I believe the more traditional method of solving this would include an ICE table maybe? I'm not sure. I was just ready to make a similar equation to that if I saw a titration like this.