Partnership
Overview
Partnership is a fundamental arithmetic topic in IBPS Clerk Prelims that tests your ability to divide profits (or losses) among business partners based on their capital contributions and time of investment.
The central idea is simple: profit share is proportional to the product of capital invested and the duration of investment. A partner who invests more money or stays invested longer deserves a larger share. Mastering this topic requires comfort with ratios and basic multiplication—no complex formulas involved. Questions range from simple two-partner splits to slightly involved three-partner scenarios with varying investment periods.
Key Concepts
- Simple Partnership: All partners invest for the same duration. Profit is divided in the ratio of their capitals alone.
- Compound Partnership: Partners invest for different time periods. Profit is divided in the ratio of (Capital × Time) for each partner.
- Capital-Time Product: The effective investment of a partner equals Capital × Number of months invested. This is the basis for all profit-sharing calculations.
- Ratio of Profit = Ratio of Effective Investments: If A's effective investment is 3 units and B's is 2 units, profits split as 3:2 regardless of the actual profit amount.
- Working Partner's Salary: Sometimes one partner manages the business and receives a fixed salary from the profit before the remainder is divided by ratio.
- Investment Changes Mid-Year: When a partner adds or withdraws capital during the year, calculate separate capital-time products for each phase and sum them.
- Joining or Leaving Partners: A partner who joins after the start or leaves before the end contributes capital only for the months they were active.
Formulas / Key Facts
Profit Share Formula Profit of A : Profit of B = (Capital_A × Time_A) : (Capital_B × Time_B)
For Simple Partnership (equal time) Profit of A : Profit of B = Capital_A : Capital_B
Three Partners A : B : C = (C_A × T_A) : (C_B × T_B) : (C_C × T_C)
When salary is involved Remaining Profit = Total Profit − Salary of working partner This remainder is then divided by ratio.
Finding individual share from ratio If ratio is a : b and total profit is P, then A's share = (a / (a + b)) × P
Quick ratio simplification tip Always reduce capital figures to simplest form before multiplying with time to keep numbers manageable.
Worked Examples
Example 1: Simple Partnership
Problem: A and B start a business with investments of Rs 40,000 and Rs 60,000 respectively. If the annual profit is Rs 25,000, find A's share.
Solution:
- Ratio of capitals = 40,000 : 60,000 = 2 : 3
- Total parts = 2 + 3 = 5
- A's share = (2/5) × 25,000 = Rs 10,000
Example 2: Compound Partnership (Different Time Periods)
Problem: A invests Rs 30,000 for 12 months. B invests Rs 45,000 for 8 months. Find the ratio in which profit should be divided.
Solution:
- A's effective investment = 30,000 × 12 = 3,60,000
- B's effective investment = 45,000 × 8 = 3,60,000
- Ratio = 3,60,000 : 3,60,000 = 1 : 1
- Profit is divided equally.
Example 3: Partner Joins Later
Problem: A starts a business with Rs 50,000. After 4 months, B joins with Rs 80,000. At the end of the year, total profit is Rs 35,000. Find B's share.
Solution:
- A's time = 12 months; B's time = 12 − 4 = 8 months
- A's effective investment = 50,000 × 12 = 6,00,000
- B's effective investment = 80,000 × 8 = 6,40,000
- Ratio = 6,00,000 : 6,40,000 = 60 : 64 = 15 : 16
- Total parts = 15 + 16 = 31
- B's share = (16/31) × 35,000 = Rs 18,064.52 ≈ Rs 18,065 (or the exact fraction if options allow)
Example 4: Working Partner Salary
Problem: A and B invest Rs 20,000 and Rs 30,000 respectively. A manages the business and receives 10% of profit as salary. Remaining profit is divided by capital ratio. If total profit is Rs 5,000, find A's total earnings.
Solution:
- A's salary = 10% of 5,000 = Rs 500
- Remaining profit = 5,000 − 500 = Rs 4,500
- Ratio = 20,000 : 30,000 = 2 : 3
- A's share from remaining = (2/5) × 4,500 = Rs 1,800
- A's total earnings = 500 + 1,800 = Rs 2,300
Common Mistakes
- Ignoring time factor: Students assume profit splits by capital alone even when investment durations differ. → Always check if all partners invested for the same period; if not, use Capital × Time.
- Miscounting months: When B "joins after 4 months," B invests for 8 months (not 4). → Subtract the delay from total period to get actual investment time.
- Forgetting to simplify ratios early: Working with large numbers like 3,60,000 : 5,40,000 leads to calculation errors. → Simplify to 36 : 54 or further to 2 : 3 immediately.
- Adding salary to ratio share incorrectly: Some students divide total profit by ratio and then add salary on top, inflating the answer. → First subtract salary from total profit, then divide the remainder.
- Confusing "months" with "years": If one partner invests for 1.5 years and another for 18 months, these are equal. → Convert all durations to the same unit before calculating.
Quick Reference
- Profit Ratio = (Capital × Time) for each partner
- Simple partnership (same time): divide by capital ratio only
- Partner joins after n months → invests for (12 − n) months
- Working partner salary is deducted first, then remainder is split
- Always simplify ratios before multiplying to avoid big numbers
- Final share = (Partner's ratio part / Sum of all parts) × Total Profit