Partnership
Profit is split by capital × time, never by capital alone. Rupee-months is the only number that matters.
Why this topic matters
Two friends start a shop. One puts in Rs 30,000, the other Rs 20,000. If the shop earns Rs 10,000, it is fair to split it 3 : 2. Partnership is just that fairness rule.
Partnership is ratio with one extra idea: money that stays in the business longer counts for more. Profit is shared in the ratio of (money × time).
Profit share = capital × time
If everyone invests for the same time, share profit in the ratio of the money invested.
If the times differ, multiply each person's money by the number of months it stayed in. Rs 10,000 for 12 months counts the same as Rs 20,000 for 6 months.
A sleeping partner only invests; a working partner also runs the business and may get a salary or a fixed % of profit first. Take that out before splitting the rest.
- A: 40,000 × 12 = 4,80,000. B: 60,000 × 8 = 4,80,000.B's money was in for 12 - 4 = 8 months.
- Ratio 1 : 1.Equal capital-months.
- B gets 17,000.
- A: 50,000 × 6 + 30,000 × 6 = 4,80,000.Split A's year into the two periods with different amounts.
- B: 30,000 × 12 = 3,60,000.
- Ratio 480 : 360 = 4 : 3.Divide by 1,20,000.
- A = 4/7 × 23,000 = 13,142.86.
Formula summary
Shortcuts and tricks
Rupee-months table
Use it when: Any partnership with changes.
- One row per partner, sum of capital × months.
- Reduce the totals to a ratio before dividing profit.
- A = 40k × 6 + 30k × 6 = 4.2 lakh. B = 7.2 lakh.
- 7 : 12, 19 parts of 2000.
- A = 14,000.
Common mistakes
Before you move on, you should be able to...
- share profit in the ratio of capital × months
- handle a partner joining late or withdrawing money midway
- take out a working partner's salary first
Practice questions (7)
Try each one before opening the solution. Or practise them one by one so your score is saved.
easy A invests Rs 20,000 for the year. B invests Rs 30,000 after 4 months. Profit Rs 18,000. B's share?
- A = 20k × 12 = 2.4 L. B = 30k × 8 = 2.4 L.
- 1:1.
Answer: Rs 9,000
medium A is a working partner getting 10% of profit as salary; the rest is split 3:2 (A:B). Profit Rs 50,000. A's total?
- Salary 5000.
- 45000 × 3/5 = 27000.
- Total 32000.
Answer: Rs 32,000
medium A starts with Rs 3,500. After 5 months B joins. Profit is split 2:3 at the year end. B's capital?
- 3500 × 12 : B × 7 = 2 : 3.
- B = 3500 × 12 × 3 / (7 × 2) = 9000.
Answer: Rs 9,000
hard A, B, C invest 5,000, 6,000, 8,000 for 12, 10, 6 months. Profit Rs 7,000. C's share?
- Rupee-months (thousands): 60, 60, 48 → 5 : 5 : 4.
- 14 parts of 500.
- C = 4 × 500.
Answer: Rs 2,000
hard Profit ratio of A, B, C is 5:7:8 and their time ratio is 3:4:5. Capital ratio?
- 5/3 : 7/4 : 8/5, x60.
Answer: 100:105:96
hard A invests 3 times B, and B invests 2/3 of what C invests. Profit Rs 6,600. B's share?
- A = 3B, C = 1.5B → 3 : 1 : 1.5 = 6 : 2 : 3.
- 11 parts of 600.
Answer: Rs 1,200
hard A and B invest in 3:5. After 4 months A withdraws half his capital. Year-end profit Rs 5,600. A's share?
- A = 3 × 4 + 1.5 × 8 = 24. B = 5 × 12 = 60.
- 24 : 60 = 2 : 5.
- 2/7 of 5600.
Answer: Rs 1,600
Class plan (2 hours, for trainers)
A tested order for teaching this topic in one 2-hour session. Present mode follows the same order.
| 10 min | Warm-up. |
| 25 min | Equal time: profit in the money ratio. |
| 30 min | Different times; joining and leaving. |
| 15 min | Adding or withdrawing midway. |
| 10 min | Working partner salary. |
| 25 min | Practice set. |
| 5 min | Recap. |