Partnership made clear.
When partners invest for different lengths of time, compare capital multiplied by time. A stated salary or fixed profit share must be handled before dividing the remaining profit.
Key concepts in Partnership
Equal duration
When investments remain for the same duration, profit shares follow the capital ratio.
Unequal duration
For the usual aptitude model, weight = capital × number of months invested.
Capital changes
Split a partner’s investment into time intervals and add the capital-month totals.
Separate payment
If the question grants a salary or commission from profit, deduct it before applying the agreed ratio to the remainder.
Investment timeline
| Partner | First 6 months | Next 6 months | Weight |
|---|---|---|---|
| A | ₹12,000 | ₹18,000 | 180000 |
| B | ₹15,000 | ₹15,000 | 180000 |
A reliable solving method
- Draw a month-by-month timeline for each partner.
- Multiply each capital amount by its own duration.
- Add intervals and simplify the weights to a ratio.
- Allocate profit and check all shares sum to the stated total.
Step-by-step solved examples
A invests ₹20,000 and B ₹30,000 for the same year. Split ₹10,000 profit.
- Capital ratio = 2:3.
- Five total parts mean ₹2,000 per part.
- A receives ₹4,000 and B ₹6,000.
A invests ₹10,000 for 12 months; B ₹15,000 for 8 months.
- A’s weight = 10000×12 = 120000.
- B’s weight = 15000×8 = 120000.
- Weights are equal, so profit is shared 1:1.
A invests ₹12,000 for 6 months, then ₹18,000 for 6 months. B invests ₹15,000 all year.
- A’s weight = 12000×6 + 18000×6 = 180000.
- B’s weight = 15000×12 = 180000.
- Profit shares are equal despite A’s changing capital.
Partnership: practice questions
Choose one answer before opening the explanation. Write down your reasoning as well as the option; a correct guess is different from a method you can repeat.
Capitals 2:3, same duration, profit ₹5,000. A gets?
Show answer and explanation — question 1
Answer B: ₹2,000
A receives 2/5 × 5000 = ₹2,000.
A: ₹6,000 for 10 months; B: ₹10,000 for 6 months. Ratio?
Show answer and explanation — question 2
Answer A: 1:1
Both weights are 60000 capital-months.
Same capital; A invests 12 months, B 9. Ratio?
Show answer and explanation — question 3
Answer C: 4:3
12:9 simplifies to 4:3.
Profit ₹14,000 split 3:4. B gets?
Show answer and explanation — question 4
Answer C: ₹8,000
4/7 × 14000 = ₹8,000.
₹2,000 salary is deducted from ₹12,000 profit; balance split equally. Salary recipient gets total?
Show answer and explanation — question 5
Answer C: ₹7,000
₹10,000 remains; half plus salary is ₹5,000+₹2,000.
A doubles capital halfway through a year. Initial capital ₹5,000. Capital-months?
Show answer and explanation — question 6
Answer B: 90000
5000×6 + 10000×6 = 90000.
Frequently asked questions
What if a partner withdraws money?
Split the timeline at the withdrawal date and use the reduced capital for the remaining months.
Does a working partner automatically receive salary?
No. Include salary only when the problem explicitly grants it.
Draw a month-by-month timeline for each partner. Allocate profit and check all shares sum to the stated total.