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I'm a bit confused about what you are asking, but 2:7 is the wrong answer.

What you are doing is diluting a dilution. The first dilution is 25% (1 part developer + 3 parts water). The second dilution is 20% of the first dilution (1 part stock solution + 4 parts water). My math isn't perfect and maybe someone will correct this, but I calculate the total working solution to be 5% strength.

If you think about it in real terms it might be easier. Say you mix 25ml developer with 75ml water (1+3) to make 100ml stock. Then you mix the 100ml of the stock solution with 400ml of water (1+4) to make a total of 500ml working solution. The total amount of concentrate in 500ml of working solution is 25ml, or 5%. This works out to 1+19.

If anyone can explain this in purely mathematical terms (how to calculate 1+3 dlluted 1+4) then please post a response.

You were doing great by converting to real life situation. The problem with ratios is that they aren't exactly fractions.

1:3 ratio == 1/4
1:4 ratio == 1/5

Take 1/4 * 1/5 and you get 1/20. or 0.25 * 0.20 = 0.05.

Another way to look at it is: 1 / 4 / 5 (1 divided by 4, divided by 5). 1 part developer divided in 4 total parts (developer and water), which is then divided again in 5 total parts (water&developer and water).

1/20 == 1:19 ratio

Hope that helps.