60-second revision
- Profit is shared in the ratio of (capital × time) for each partner.
- Simple partnership (equal time): profit ratio = capital ratio.
- A partner who joins after m months in a 12-month year is counted for (12 - m) months.
- With a withdrawal or extra investment, add each period separately: capital1 × months1 + capital2 × months2.
- A working partner's salary or commission is taken out first; only the rest is shared by investment.
- Time ratio = (profit share ÷ capital) for each partner; capital ratio = (profit share ÷ time).
- Rent of a pasture is shared in the ratio of (animals × months).
The one rule
Each partner's share of profit (or loss) is proportional to capital × time. When everyone invests for the same period (simple partnership), this reduces to the ratio of capitals. When periods differ (compound partnership), multiply each capital by its months.
| Type | Profit ratio | Example |
|---|---|---|
| Simple | Capital ratio | Capitals 4:5:6, profit Rs 30,000: shares 8,000, 10,000, 12,000 |
| Compound | Capital × months | A Rs 20,000 for 12 months, B Rs 36,000 for 7 months: 240:252 = 20:21 |
In the compound example, a profit of Rs 41,000 splits as Rs 20,000 for A and Rs 21,000 for B.
Joining late and leaving early
- If B joins 5 months after the business starts, B's money works for 12 - 5 = 7 months of the year.
- If A leaves after 8 months, A's money works for 8 months.
- Read carefully whether the question says "after 5 months" (counted 7 months) or "for 5 months".
Withdrawals and additions
Split the year into periods and add capital × months for each. Example: A starts with Rs 60,000 and withdraws Rs 20,000 after 4 months. A's total = 60 × 4 + 40 × 8 = 560 (in thousand-rupee months). If B puts in Rs 50,000 for the whole year, B = 50 × 12 = 600, so A:B = 560:600 = 14:15.
Working (active) partner and sleeping partner
A sleeping partner only invests. A working partner may get a salary or a share of profit for managing the business; this is paid first, and the remaining profit is divided in the investment ratio.
Worked example: profit Rs 40,000. A, the working partner, gets 10% for management, i.e. Rs 4,000. The remaining Rs 36,000 is shared in the capital ratio 5:4, so A gets 20,000 and B gets 16,000. A's total = Rs 24,000.
If the salary is monthly (say Rs 2,000 a month), take out Rs 24,000 for the year first.
Working backwards: time or capital
- Time ratio = (share ÷ capital) for each. Capitals 3:4 and profits 9:16 give times (9/3):(16/4) = 3:4.
- Capital ratio = (share ÷ time) for each. Profits 2:3 and times 4:9 give capitals (2/4):(3/9) = 1/2 : 1/3 = 3:2.
Rent sharing (pasture problems)
Grazing rent is shared like a partnership, with animals in place of capital. A grazes 8 cows for 6 months and B grazes 12 cows for 5 months: 48:60 = 4:5. A rent of Rs 2,700 is split as Rs 1,200 and Rs 1,500.
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