If you increase the amount of the boiling water and tap water twice, will their temperature change?

No, the temperature will not change if you increase the amount of boiling water and tap water twice, assuming that the tap water is the same temperature each time.  Let me explain:

• Let's say we've got 100 ml of boiling water (100C), and 100 ml of tap water (we'll call it 10C).  If we mix the two together, we've now got 200 ml of water at 55C temperature.
  
• Now, if we then mix another 100 ml of boiling water (100C), and 100 ml of tap water (10C), we've got another 200 ml of water at 55C temperature.
  
• If we then combine the two together, we've got a total 400 ml of water at 55C temperature.
  

Of course, if the tap water temperature changed each time, you would be left with a very different result.  You also need to take into consideration that the original batch of water would have to be kept at 55C, otherwise it would cool over time and alter the result.

Your question has made me wonder about the temperature of tap water, and then I remembered that I'd recently watched a documentary on the results of fracking.  This woman's tap water can be set on fire! That would certainly throw a spanner in the works of your experiment!