Partnership Formulas, Profit Sharing and Questions
Partnership questions use the capital invested by each partner and the time for which it remains invested. The profit sharing ratio is found by multiplying capital by investment time. This page explains partnership formulas, changing investments, admission or withdrawal of partners, and methods for calculating each partner’s profit or loss.
What is Partnership in Quantitative Aptitude?
If partners invest capitals C1, C2, C3 for times T1, T2, T3, their profit sharing ratio is C1T1 : C2T2 : C3T3. When all partners keep their capital invested for the same time, the ratio becomes their capital ratio. For example, investments of ₹8,000 and ₹12,000 for equal periods give a profit ratio of 8,000 : 12,000 = 2 : 3.
Partnership Formula & Tricks
Important Formulas
Multiply each partner’s invested capital by the number of months or years for which it remains invested.
If the ratio is a : b, the first partner receives a/(a+b) of the total profit.
Loss is divided in the same ratio as profit unless a different agreement is stated.
When all partners invest for the same duration, time cancels and profit is shared in the capital ratio.
For equal profit shares, each partner’s capital-time product must be equal.
Quick Tricks
Convert every investment period into the same unit before multiplying it by capital. Months are usually convenient when a partner joins or withdraws during a year.
Calculate only the relative products and cancel common factors before finding the profit. The actual rupee values are not needed for the ratio.
Treat each investment period separately and add the capital-time products for that partner. This handles additions and withdrawals accurately.
Partnership Concepts
Profit Sharing Ratio from Capital and Time
For partners A and B, calculate A’s capital × A’s time and B’s capital × B’s time. Reduce these products to their simplest ratio. If A invests ₹20,000 for 9 months and B invests ₹15,000 for 12 months, the ratio is 20,000 × 9 : 15,000 × 12 = 180,000 : 180,000 = 1 : 1.
Distribution of Profit or Loss
If the ratio of A, B and C is 2 : 3 : 5 and the total profit is ₹20,000, the sum of ratio terms is 10. Their shares are ₹4,000, ₹6,000 and ₹10,000 respectively. The same calculation applies to a loss.
Changing Capital During the Partnership
For each section, use capital × number of months. Add the products belonging to the same partner, then compare the totals. A partner who invests ₹10,000 for 12 months has a product of 120,000; a partner investing ₹15,000 for 4 months and ₹5,000 for 8 months has a product of 60,000 + 40,000 = 100,000. Their ratio is 120 : 100 = 6 : 5.
Admission or Withdrawal of a Partner
Use the exact duration for which each partner’s capital remains in the business. If A invests ₹12,000 for 12 months and B joins with ₹18,000 for the last 8 months, the ratio is 12,000 × 12 : 18,000 × 8 = 144,000 : 144,000 = 1 : 1.
Salary, Commission and Remaining Profit
Suppose total profit is ₹50,000, A receives a fixed salary of ₹8,000, and the remaining amount is shared by A and B in the ratio 2 : 3. The distributable profit is ₹42,000. A receives ₹8,000 + ₹16,800 = ₹24,800, while B receives ₹25,200.
Partnership Video Lessons
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Investment in Ratio Problems
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Partnership Revision Points
Use these rules to solve partnership aptitude questions quickly and accurately.
- Profit sharing ratio = Capital × Investment time.
- Use the same time unit for every partner, usually months.
- For equal investment periods, profit ratio equals the capital ratio.
- For changing capital, calculate each period separately and add the products.
- Individual share = Total profit or loss × Individual ratio term ÷ Sum of ratio terms.
- A newly admitted partner is considered only for the period after joining.
- A withdrawing partner is considered only for the period before withdrawal.
- For a fixed salary or commission, deduct it first if the question states that it is paid before sharing the remaining profit.
Partnership FAQs
What is the basic partnership formula?
The basic formula is profit sharing ratio = capital × time. For partner A, the contribution is A’s capital multiplied by the period of investment.
How is ₹36,000 profit divided in the ratio 2 : 3 : 4?
The ratio sum is 9. The shares are ₹36,000 × 2/9 = ₹8,000, ₹12,000 and ₹16,000.
What is the profit ratio if A invests ₹5,000 for 12 months and B invests ₹8,000 for 6 months?
A’s product is 60,000 and B’s product is 48,000. The ratio is 60,000 : 48,000 = 5 : 4.
How do you handle a partner who joins midway through the year?
Count the partner’s capital only for the months after joining. For example, ₹10,000 invested for the last 6 months contributes 60,000 to the capital-time ratio.
When does the partnership profit ratio equal the capital ratio?
It equals the capital ratio when all partners keep their capital invested for the same period.
How are losses divided in a partnership question?
Unless another agreement is given, losses are divided in the same capital-time ratio as profits.