The non existence of any written agreement in your case is not at all pose any impediment for the purpose of creating 'partnership.'. Please note that for the purpose of partnership the ingredients are like-
1.Agreement between the persons
2.They must be carrying on business at that time .
3. Motive should be for the purpose of sharing profit
4.Relation between them is of mutual agency.
Now we all know that contract can be made by words spoken or writtten.
So in your case if the activities of the concerned persons are fulfilling the above criteria then subsequent execution of a formal deed of partnership authenticating their nature of patnership already in force is not a stumbling block and hence the bid is legal.
As per section 13 the profit and loss of the partners are to be divded equally unless otherwise provided.