Partners joining, leaving or changing investment

Outcome

Allocate profit when partners join, leave or change their capital.

Concept and assumptions

Use a 12-month accounting period. After k completed months, 12 − k months remain. A departing partner withdraws all capital and contributes zero thereafter.

Profit follows capital-time weights, with no salary or commission unless stated. Profits are not reinvested.

Weight = sum of (capital in each interval × months in that interval).

Partition time without gaps or overlaps. Additions increase subsequent capital; withdrawals reduce it. Summing interval weights works because each interval supplies its own capital-time contribution.

Profit share = sharing pool × individual weight ÷ total weight.

Deduct an agreed salary first only when instructed; add it to that partner’s share. Closing capital alone cannot represent the year.

Worked examples

Example 1 — Joining later. A invests ₹60,000 throughout the year. B invests ₹90,000 after 4 completed months and stays until year-end. Divide ₹64,000.

B participates for 12 − 4 = 8 months. Weights: A = 60,000 × 12 = 720,000; B = 90,000 × 8 = 720,000. Ratio = 1:1. Each receives 64,000 ÷ 2 = ₹32,000.

Example 2 — Joining and leaving. A invests ₹50,000 throughout. B invests ₹80,000 initially but leaves after 9 completed months. C invests ₹60,000 after 6 completed months. Profit is ₹70,000.

C invests for 12 − 6 = 6 months. Weights = (50,000 × 12):(80,000 × 9):(60,000 × 6) = 600,000:720,000:360,000 = 5:6:3. Total parts = 14; one part = 70,000 ÷ 14 = 5,000. A = 5 × 5,000 = ₹25,000; B = 6 × 5,000 = ₹30,000; C = 3 × 5,000 = ₹15,000.

Example 3 — Changing capital with salary. A starts with ₹80,000, adding ₹40,000 as month 4 begins. B starts with ₹100,000, withdrawing ₹40,000 as month 7 begins. C joins with ₹60,000 as month 5 begins. All remain thereafter. Profit before A’s agreed annual salary is ₹138,000; pay A ₹23,000 first.

A’s weight = 80,000 × 3 + 120,000 × 9 = 1,320,000. B’s weight = 100,000 × 6 + 60,000 × 6 = 960,000. C’s weight = 60,000 × 8 = 480,000. Ratio = 11:8:4; total parts = 23. Sharing pool = 138,000 − 23,000 = 115,000. One part = 115,000 ÷ 23 = 5,000. Profit shares: A = 11 × 5,000 = ₹55,000; B = 8 × 5,000 = ₹40,000; C = 4 × 5,000 = ₹20,000. A’s total = 55,000 + 23,000 = ₹78,000; B receives ₹40,000, C ₹20,000.

Common mistakes

Miscounting months; confusing added capital with the new balance; counting capital after departure; inventing salary payments; sharing the pre-salary total again.

Practice questions

1. A invests ₹40,000 throughout; B invests ₹60,000 after 6 completed months. Divide ₹42,000.
2. A invests ₹60,000 throughout; B invests ₹80,000 initially and leaves after 6 completed months. Divide ₹50,000.
3. A invests ₹50,000 initially, adding ₹30,000 after 4 completed months. B invests ₹60,000 throughout. Divide ₹78,000.
4. A invests ₹60,000 throughout; B invests ₹90,000 after 6 completed months. Profit before A’s agreed annual salary of ₹14,000 is ₹98,000. Pay salary first; find both total receipts.

Worked answers

1. B’s duration = 6 months. Weights = 480,000:360,000 = 4:3. A = 42,000 × 4/7 = ₹24,000; B = 42,000 × 3/7 = ₹18,000.
2. Weights = 60,000 × 12 : 80,000 × 6 = 720,000:480,000 = 3:2. Shares = 50,000 × 3/5 = ₹30,000 and 50,000 × 2/5 = ₹20,000.
3. A’s weight = 50,000 × 4 + 80,000 × 8 = 840,000. B’s = 60,000 × 12 = 720,000. Ratio = 7:6. Shares = 78,000 × 7/13 = ₹42,000 and 78,000 × 6/13 = ₹36,000.
4. Weights = 720,000:540,000 = 4:3. Pool = 98,000 − 14,000 = 84,000. A’s profit share = 84,000 × 4/7 = 48,000; total = 48,000 + 14,000 = ₹62,000. B receives 84,000 × 3/7 = ₹36,000.