Partnership Profit with Unequal Periods
Three friends start a small printing business. Anwar invests 60,000 taka at the start. Bina invests 45,000 taka at the start but withdraws her entire capital after 8 months. Chand invests nothing at the start but puts in 90,000 taka after 4 months and keeps it until the end of the year. At year end the business earns a profit of 1,32,000 taka before any distribution. The friends had also agreed that Anwar, who manages the shop, would first receive a salary of 12,000 taka from the profit, and the remaining profit would be shared in proportion to capital-months. A dispute arises: Bina claims her share should be based on her full 45,000 for the whole year because she was a partner from day one.
1. Compute each partner's capital-months and the ratio in which the distributable profit should be shared.
Read the worked answer
Capital-months = capital × number of months the money stayed invested.
- Anwar: 60,000 × 12 = 7,20,000 capital-months.
- Bina: 45,000 × 8 = 3,60,000 capital-months (her money was withdrawn after 8 months, so only 8 months count).
- Chand: 90,000 × 8 = 7,20,000 capital-months (invested from month 5 to month 12, i.e. 8 months).
Ratio = 7,20,000 : 3,60,000 : 7,20,000 = 2 : 1 : 2.
Bina's claim is incorrect: in a partnership, profit share follows capital-months, not mere membership duration. Her withdrawal after 8 months reduces her weight.
2. After paying Anwar's salary, find each partner's profit share in taka.
Read the worked answer
Distributable profit = 1,32,000 − 12,000 = 1,20,000 taka.
Ratio 2 : 1 : 2, total parts = 5.
- Each part = 1,20,000 ÷ 5 = 24,000 taka.
- Anwar: 2 parts = 48,000 taka (plus 12,000 salary = 60,000 total received).
- Bina: 1 part = 24,000 taka.
- Chand: 2 parts = 48,000 taka.
Check: 48,000 + 24,000 + 48,000 = 1,20,000. Correct.
3. Bina argues she should instead get a share proportional to her capital-month if the salary were not paid. Show numerically whether removing the salary would change the ratio, and state what Bina actually receives overall as a percentage of total profit.
Read the worked answer
The ratio depends only on capital-months, not on the size of the profit pool. Removing the salary changes the pool (from 1,20,000 to 1,32,000) but not the ratio 2 : 1 : 2.
Without salary, Bina would get 1/5 × 1,32,000 = 26,400 taka. With salary, she gets 24,000 taka. The salary reduces her absolute share because it shrinks the pool, but her proportional claim (1/5 of distributable profit) is unchanged.
Bina's overall share as a percentage of total profit = 24,000/1,32,000 × 100 ≈ 18.18%.
Anwar receives 60,000/1,32,000 ≈ 45.45% and Chand 48,000/1,32,000 ≈ 36.36%. Sum ≈ 100%. So Bina's argument fails: her 1/5 ratio is correct, and the salary legitimately reduces her cash.