Partnership Exit
Quantitative aptitude

Partnership

Profit is split by capital × time, never by capital alone. Rupee-months is the only number that matters.

Start with this

Two friends start a shop. One puts in Rs 30,000, the other Rs 20,000. If the shop earns Rs 10,000, it is fair to split it 3 : 2. Partnership is just that fairness rule.

Partnership is ratio with one extra idea: money that stays in the business longer counts for more. Profit is shared in the ratio of (money × time).

Profit share = capital × time

If everyone invests for the same time, share profit in the ratio of the money invested.

If the times differ, multiply each person's money by the number of months it stayed in. Rs 10,000 for 12 months counts the same as Rs 20,000 for 6 months.

A sleeping partner only invests; a working partner also runs the business and may get a salary or a fixed % of profit first. Take that out before splitting the rest.

A30,000 x 12B20,000 x 12
Same time: profit 3 : 2

Profit share = capital × time: the rules

Share ratio = C1 × T1 : C2 × T2 : ...
Capital times months.
Working partner: salary first, then split the rest
Read carefully what is paid before the split.

Worked example

A invests Rs 40,000 for a year. B joins after 4 months with Rs 60,000. The year's profit is Rs 34,000. B's share?

  1. A: 40,000 × 12 = 4,80,000. B: 60,000 × 8 = 4,80,000.
    Why: B's money was in for 12 - 4 = 8 months.
  2. Ratio 1 : 1.
    Why: Equal capital-months.
  3. B gets 17,000.

Answer: 17000

Worked example

A and B start with Rs 50,000 and Rs 30,000. After 6 months A withdraws Rs 20,000. Profit at year end is Rs 23,000. Find A's share.

  1. A: 50,000 × 6 + 30,000 × 6 = 4,80,000.
    Why: Split A's year into the two periods with different amounts.
  2. B: 30,000 × 12 = 3,60,000.
  3. Ratio 480 : 360 = 4 : 3.
    Why: Divide by 1,20,000.
  4. A = 4/7 × 23,000 = 13,142.86.

Answer: 13,142.86

Shortcut: Rupee-months table

Use it when: Any partnership with changes.

  1. One row per partner, sum of capital × months.
  2. Reduce the totals to a ratio before dividing profit.

Rupee-months table: try it

A: 40,000 all year but withdraws 10,000 after 6 months. B: 60,000 all year. Profit 38,000. A's share?

  1. A = 40k × 6 + 30k × 6 = 4.2 lakh. B = 7.2 lakh.
  2. 7 : 12, 19 parts of 2000.
  3. A = 14,000.

Answer: Rs 14,000

Common mistakes

Using the money ratio when the partners were in for different months.
Multiply each amount by its months.

Your turn hard

A, B, C invest 5,000, 6,000, 8,000 for 12, 10, 6 months. Profit Rs 7,000. C's share?

  1. Rupee-months (thousands): 60, 60, 48 → 5 : 5 : 4.
  2. 14 parts of 500.
  3. C = 4 × 500.

Answer: Rs 2,000

Your turn medium

A is a working partner getting 10% of profit as salary; the rest is split 3:2 (A:B). Profit Rs 50,000. A's total?

  1. Salary 5000.
  2. 45000 × 3/5 = 27000.
  3. Total 32000.

Answer: Rs 32,000

Your turn hard

Profit ratio of A, B, C is 5:7:8 and their time ratio is 3:4:5. Capital ratio?

  1. 5/3 : 7/4 : 8/5, x60.

Answer: 100:105:96

Your turn medium

A starts with Rs 3,500. After 5 months B joins. Profit is split 2:3 at the year end. B's capital?

  1. 3500 × 12 : B × 7 = 2 : 3.
  2. B = 3500 × 12 × 3 / (7 × 2) = 9000.

Answer: Rs 9,000

Recap

Now practise

7 questions with full solutions.

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