Thank you for using the site. I'll be happy to help you with this if I can.
Do you have any additional information regarding the terms of the partnership? Is there any chance that specific knowledge of laws concerning partnerships in the UK is required?
Is this problem from a math course?
Assuming that the 50% partnership means that they share total earnings and expenses equally, then the calculation would look like this.
Note that I am also assuming that each partner has retained their own earnings, and has paid their own expenses, and they are now "settling up" the account to balance things out.
Total income is £ 90588, which means that each should receive £ 90588 / 2 = £ 45294.
Partner B's income is short by £ 45294 - £ 29095 = £ 16199
Similarly, each should be accountable for half of the total expenses, or £ 93470 / 2 = £ 46735
Partner B has overpaid expenses by £ 63633 - £ 46735 = £ 16898
Partner A would need to make up for Partner B's shortfall in income, and Partner B's over-payment of expenses.
Partner A thus owes Partner B a total of: £ 16199 + £ 16898 = £ 33097
Please feel free to ask if you have any questions about this solution.