Partnership: Concepts, Formulas, and Clear Examples

Partnership splits profit (or loss) in ratio of capital × time invested. Simple partnership: same time period → split by capitals only.

Working partner may get salary first; remaining profit splits by capital ratio.

Convert months to a common time unit before multiplying capital × time.

Capital ratio profit share

Same duration

$$\text{Share}_A : \text{Share}_B = C_A : C_B$$

Different times

$$\text{Share}_A : \text{Share}_B = C_A T_A : C_B T_B$$

Example — Different months

A ₹12000 for 8 mo, B ₹9000 for 12 mo. Ratio = $12000\cdot8 : 9000\cdot12 = 96000:108000 = 8:9$.

Salary + profit split

• Subtract working partner salary from total profit, then split remainder.

Loss sharing

• Loss ratio equals capital-time ratio unless agreement says otherwise.

Joining/leaving mid-year

• Break into segments or use effective capital-months.

Compound partnership

• Three partners: sum shares = total profit after adjustments.

Verification

• Individual shares must add to total profit.
• Check time in months vs years.

Step-by-step method for exam questions

1. List each partner’s capital and months active.
2. Compute capital × time weights.
3. Form ratio; simplify.
4. Apply salary deduction if any.
5. Multiply total profit by fraction of ratio.
6. Pick option.

Formula cheat sheet

Frequently asked questions

Interest on capital?

Some problems pay interest first; read stem for order.

Different currencies?

Convert to one currency before ratio.

Sleeping partner?

Usually no salary; profit by capital-time only.

Mid-year join?

Count only months present; or split periods.

Practice on this platform

Use 4 practice sets (10 MCQs, detailed solution after each answer) and 2 timed mocks (20 minutes) on this topic to convert formulas into speed and accuracy.