On which of the following bases the profit can be calculated for the retiring partner for the intervening period if he retires in the middle of the year?

Any of these

Profit can be calculated on any of the above basis. The base can be mentioned in the partnership deed or it will be mutually decided by the partners. Closing the books and preparing the final accounts for the period following the death of a partner can be a complex and time-consuming process. To simplify this procedure, the deceased partner's share of the profit can be determined using alternative methods.
One approach is to calculate their share based on the previous year's profit.
Alternatively, an average of profits from the past few years can be used.
Another option is to base the calculation on the sales generated during the period. These alternative methods help streamline the process and provide a reasonable estimation of the deceased partner's share of the profit.