Math questions

January and February will contain some payments from November and December?
Can you work back from June (and May) to see how much they were?

It helps to think of each purchase as a 3 month window (1/2, 1/4, 1/4).

Okay, so this is as far as I have got.
June: 2000 is 1/4 of the amount in April. Therefore, April has 8000? Since only half of 8000 is paid in April we should have only 4000 in April but instead, we have £5000. So there is an extra £1000 from previous months?

Thats the right idea.
Think about June's conribution of 2k this means April May June (4k, 2k 2k). So the remainder is
(9k 3K 4k 1k 1k 0k)
Now Mays contribution of 1k must be (2k 1k 1k). So the remainder is ...

4k 2k 2k

What do you mean?

"Now Mays contribution of 1k must be (2k 1k 1k). So the remainder is ..."
What I understood from this is.

March -- April -- May
2k -- 1k -- 1k

So subtract from (9k 3K 4k 1k 1k 0k) to give
(9k 3K 2k 0k 0k 0k)
April payments are 0k so ?

Feb March April: 4k 2k 2k
Sorry I just realised. If April is 0K.
Then
Feb March April (0k 0k 0k)
I've attached a picture of where I have got upto but it is still wrong

youre pic is correct but youre adding up the wrong parts.
The !1/2 spend in jan,feb,mar,apr is 4+0+2+2 = 10. So double to get 20.

Thats correct.
Ive a typo in the previous post for April. Will correct now ...

Sure but in 9 matches 90 points is ahared amongst 4, so 22.5 each, on average. The highest two have ~6 points more than third and they have ~6 points more than last. Then the last person gets 6 in the final match. Can you fill in the details?

Going with this,
On the 9th round, this is what it should be like:
1) 28
2) 28
3) 22
4) 16
I'm still quite unsure as to what I am doing

It would be approximately that, though the scores have to be achievable and no ties. Why are you unsure - the scores have to reflect the info in the question and the highest losing score must mean they score 6 in the last match.

Suppose on the 10th round, last place scores a 6, then this would get it to around 22, which isn't an option. Alternatively, we would have to guess. Since we are using rough values, the answer could be C, D or E. Going by with the logic that we are currently using.

No, those scores mean there could be ties, depending on the last match. What scores make ties impossible (with the last one as high as possible).