Capital, time and a late entrant at a three-partner firm
On 1 April, Asha, Bina and Charu start a small loan-advisory firm. Asha contributes ₹80,000 on day one. Bina joins on 1 August with ₹1,20,000, and Charu joins on 1 November with ₹60,000. The partnership deed says only that 'profits shall be shared in proportion to the capital contributed by each partner'. It says nothing about duration, salary or drawings, and no partner has drawn a salary. The year closes on 31 March with a net profit of ₹4,81,000 after all expenses. Before the profit is credited, Charu asks for a fresh reading of the deed, and Bina argues that because she put in the largest single sum she should receive the largest share. Asha wants the numbers settled on paper, with reasons, not on seniority.
1. Compute each partner's share treating 'capital contributed' as capital actually at risk, i.e. weighted by the months it stayed in the firm.
Read the worked answer
Weight each contribution by the months it remained invested (1 April to 31 March is 12 months, 1 August to 31 March is 8 months, 1 November to 31 March is 5 months):
| Partner | Capital | Months | Capital-months |
|---|---|---|---|
| Asha | ₹80,000 | 12 | 9,60,000 |
| Bina | ₹1,20,000 | 8 | 9,60,000 |
| Charu | ₹60,000 | 5 | 3,00,000 |
Ratio = 96 : 96 : 30 = 16 : 16 : 5, total 37 parts. ₹4,81,000 ÷ 37 = ₹13,000 per part.
- Asha: 16 × 13,000 = ₹2,08,000
- Bina: 16 × 13,000 = ₹2,08,000
- Charu: 5 × 13,000 = ₹65,000
Note what this does to Bina's argument: her ₹1,20,000 for 8 months is exactly the same capital-months as Asha's ₹80,000 for 12 months, so their shares are identical. The size of a single cheque is not the measure.
2. Now compute the shares under a literal reading of 'proportion to the capital contributed' (amount only, ignoring time) and quantify who gains and who loses against your first answer.
Read the worked answer
Amounts only: 80,000 : 1,20,000 : 60,000 = 4 : 6 : 3, total 13 parts. ₹4,81,000 ÷ 13 = ₹37,000 per part.
- Asha: 4 × 37,000 = ₹1,48,000
- Bina: 6 × 37,000 = ₹2,22,000
- Charu: 3 × 37,000 = ₹1,11,000
Against the time-weighted answer:
- Asha: 1,48,000 − 2,08,000 = ₹60,000 worse off
- Bina: 2,22,000 − 2,08,000 = ₹14,000 better off
- Charu: 1,11,000 − 65,000 = ₹46,000 better off
The two readings differ by ₹1,20,000 moving from Asha to the two late entrants, which is precisely the value of the extra months Asha's money was exposed. A literal reading rewards the size of a contribution; a time-weighted reading rewards the risk actually carried.
3. Charu proposes taking 10% of the profit as a manager's salary before the balance is split on the time-weighted basis. He says this costs the others nothing because 'the salary comes out of my share.' Test that claim against the first answer.
Read the worked answer
Salary: 10% of ₹4,81,000 = ₹48,100. Balance = ₹4,32,900, split 16 : 16 : 5 (37 parts). ₹4,32,900 ÷ 37 = ₹11,700 per part.
- Asha: 16 × 11,700 = ₹1,87,200
- Bina: 16 × 11,700 = ₹1,87,200
- Charu: 5 × 11,700 + 48,100 = 58,500 + 48,100 = ₹1,06,600
Change against the first answer:
- Asha: 1,87,200 − 2,08,000 = −₹20,800
- Bina: −₹20,800
- Charu: 1,06,600 − 65,000 = +₹41,600
The changes sum to zero, which shows the claim is false. The salary is carved out of the common pool before sharing, so Asha and Bina each fund it. What Charu actually gains (₹41,600) is his salary less the share of the pool he gives up (₹6,500 of the 5-part slice he would otherwise have taken). If a salary is genuinely intended, it should be fixed as a stated amount or a share of gross receipts and agreed in the deed, not derived from the profit it is meant to leave untouched.