Formula
Profit is shared in the ratio of capital time
Arithmetic • Profit and Loss • Partnership
Formula
When partners invest for unequal periods, profit is divided in the ratio of their capital-months: a partner who holds capital for time over successive spells carries weight .
How to use it
- 1Break each partner's year into spells of constant capital and add across the spells.
- 2Reduce the resulting weights to lowest terms before dividing the profit; the parts should then sum to a divisor of the profit.
- 3If every partner invests for the same period, the time cancels and the split is by capital alone.
Worked example
invests Rs. for a whole year; invests Rs. for the last months only. A profit of Rs. is shared. What does receive?
Step-by-step
- 1;
Why: Weight each capital by the number of months it was employed.
- 2, so Rs. splits into parts of Rs.
- 3receives
Answer
Rs.
Watch out
A withdrawal or an injection starts a new spell, and the capital before and after must be weighted separately rather than averaged. A fraction 'of his stock' means of that partner's own investment, not of the joint capital.
Builds on
Also known as
partnership, capital-months, profit sharing ratio, investment times time, equivalent capital