Core rule
Profit is shared in the ratio of capital x time (the investment in "rupee-months"). If all partners invest for the same time, profit is in the ratio of capitals. Target: 40 seconds.
Key formulas
| Situation | Share ratio |
|---|---|
| Capitals C1, C2 for same time | C1 : C2 |
| Capitals C1, C2 for times T1, T2 | C1 T1 : C2 T2 |
| Capital changes during the year | sum of (capital x months) for each phase |
| Working partner gets salary s% of profit | remaining (100 - s)% shared by capital ratio |
| Profit ratio and time ratio given | capital ratio = profit ratio / time ratio (term by term) |
Joining late or leaving early
- A partner who joins after 4 months invests for 8 months of a 12-month year.
- A partner who withdraws half the capital after 6 months: (C x 6) + (C/2 x 6).
- "After another 3 months" counts from the previous event - read the timeline carefully.
Worked example
A invests Rs. 50,000 for the whole year; B joins after 3 months with Rs. 40,000. Profit = Rs. 32,000.
A : B = 50,000 x 12 : 40,000 x 9 = 6,00,000 : 3,60,000 = 5 : 3. A gets 32,000 x 5/8 = Rs. 20,000, B gets Rs. 12,000.
Worked example 2 (working partner)
A and B have capitals in ratio 3 : 2. A gets 10% of profit as salary. A's total = 16,000. A's fraction = 10% + 3/5 of 90% = 64%, so profit = 16,000/0.64 = Rs. 25,000.
Worked example 3 (relations between capitals)
A invests 3 times B, and B invests 2/3 of C. Put C = 3: B = 2, A = 6. Ratio 6 : 2 : 3.
Common traps
- Ignoring time and sharing only by capital.
- Counting months wrongly when a partner joins "after 4 months" (it is 8 months, not 4).
- Applying the salary percentage to the remainder instead of the whole profit (read which one is meant).
- Interest on capital: deduct it first, then share the rest.
Worked example 4 (finding the capital ratio)
Profits are in the ratio 2 : 3 and the investment periods are in the ratio 4 : 5. Capital ratio = 2/4 : 3/5 = 10 : 12 = 5 : 6.
Worked example 5 (equal share)
A invests Rs. 40,000 for 12 months. B joins after 4 months and wants an equal share of the profit. B's capital x 8 = 40,000 x 12, so B must invest Rs. 60,000.