wrote:

This is not school homework but an interesting situation I came
across.

What do you mean? A situation is real life? What property can you
buy in London for 100 pounds which is going to yield 20 pounds a year?

1) John bought income property A in London in 2005 for 100 pounds,
2) Dave bought income property B in Liverpool in 2006 for 60 pounds,
inflation was 10% up from previous year

OK, so you are saying that property A was worth 110 pounds in 2006.

John & Dave became mutually partners on the AB = A+B pie.

OK, so you are saying that in 2006, the two properties together were
worth 170 pounds.

What % each does own of the pie?

That's an impossible question to answer, because there are at least
three different ways in which the properties can be valued. One way
is by how much they can be expected to sell for. That's 110 and 60
pounds, so the percentages would be 64.7 and 35.3. Another way is by
their income generating capacity. If that's still 20 and 15 pounds
per year, then the percentages will be 57.1 and 42.9. Yet another
is by their capacity for accumulating capital gain.

All of these need to be taken into account when John and Dave sit
down to negotiate and decide what they're going to do.

Next,

3) Larry bought income property C in Manchester in 2007 for 75 pounds,
inflation was up 5% from previous year.

NOW, the 3 want to become mutually partners where the pie now is ABC =
A+B+C. What % each should have?

Different numbers, but same answer.