When Capital Changes During the Period

Often a partner does not keep the same amount of capital in the business for the whole period — they may put in more money partway through, or withdraw part of what they invested. In such a case that partner's contribution is worked out stretch by stretch: for each period during which the capital stayed at one fixed amount, form the product (capital during that stretch) × (length of that stretch), and then add these products together to get the partner's total capital-time contribution for the whole period.

For a partner whose capital was $A$ for a time $t_1$ and then changed to $B$ for a further time $t_2$, the total contribution is $A\,t_1 + B\,t_2,$ and this single number is used as that partner's term in the profit-sharing ratio, alongside the corresponding capital-time totals of the other partners.

For example, a partner who invests $8000$ rupees for the first $6$ months and then withdraws $2000$ rupees — leaving $6000$ rupees — for the remaining $6$ months of a year contributes $8000\times 6 + 6000\times 6 = 48000 + 36000 = 84000 \text{ capital-months}.$ A partner who adds money instead of withdrawing it is handled in exactly the same way, with the larger amount used for the later stretch. …