"Ronald Raygun" wrote
Doing it differently would not necessarily
be unfair, just fair in a different way.

Although we are told that the total income is unchanged at 52
pounds per year, and we can perhaps assume that this means
the income generated by each property is also unchanged at
20/15/17 pounds per year, we are not told whether and how
the properties' value has changed since they were bought.
One fair way to split ownership is in proportion to the value...

"Tim" wrote:
Well, obviously (in such an idealised example!), property A
will have fallen in value to 80 pounds in 2006 and then property
A will have increased in value to 88.24 pounds in 2007 and
property B will have increased in value to 66.18 pounds in 2007.
[They will also each have changed by the same factor from 2007 to 2008.]

Thus the fair ownership proportions (in proportion
to the values) are still: 88.24 / 229.41 = 38%,
66.18 / 229.41 = 29% and 75.00 / 229.41 = 33%.

"Ronald Raygun" wrote
While it was easy enough for you to make up a set of value movements
which made the 2007/8 value proportions the same as the income ones, ...

It's not a matter of "making up" the value movements, but
rather *calculating* them from their yield. Of course, the
*actual* yields were not quoted for property A in 2006 or
2007, nor for property B in 2007, so the yields that were
known instead were used as reasonable proxies (yield in
2006 from property B, yield in 2007 from property C).

"Ronald Raygun" wrote
... the underlying assumption that the value inflation rates are the same
in each of the three locations in any one year is a pretty unrealistic.

Of course, but in the absence of further information (the question
had no other data), it's got to be the best assumption, hasn't it?

"Ronald Raygun" wrote
"Idealised" indeed!

;-)