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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

  1. 1Break each partner's year into spells of constant capital and add across the spells.
  2. 2Reduce the resulting weights to lowest terms before dividing the profit; the parts should then sum to a divisor of the profit.
  3. 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. 1
    ;

    Why: Weight each capital by the number of months it was employed.

  2. 2
    , so Rs. splits into parts of Rs.
  3. 3
    receives

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

Appears in past papers

2020 (II)

2018 (I)

2016 (II)