Quick Concept Summary
Partnership is ratio and proportion with one extra idea: money earns according to both amount invested and duration invested.
Worked Examples
Example 1
A invests Rs. 40,000 for 12 months and B invests Rs. 60,000 for 8 months.
A:B = 40000x12 : 60000x8 = 480000 : 480000 = 1:1
Example 2
A and B invest in the ratio 3:5. Total profit is Rs. 24,000.
A's share = 24000 x 3/8 = 9000
B's share = 15000
Question Types
- Same time, different capital
- Different time, same capital
- New partner joins later
- Capital withdrawn midway
Practice Questions
1. A invests Rs. 20,000 for 12 months and B Rs. 30,000 for 8 months. Find the ratio. 2. A, B, C invest in ratio 2:3:5. Profit is Rs. 50,000. Find C's share. 3. A invests Rs. 40,000. After 4 months, B joins with Rs. 60,000. Find their year-end ratio.
Common Mistakes
- Comparing only capital and ignoring time
- Forgetting to convert all durations into the same unit
- Using the ratio before handling mid-year changes