How to Solve Partnership Problems
Solve partnership aptitude problems using the capital × time profit-sharing ratio — with a worked example and practice questions with answers.
Expected Interview Answer
Partnership problems split profit in the ratio of each partner’s capital multiplied by the time it was invested, so the profit-sharing ratio is capital₁ × time₁ : capital₂ × time₂, not simply the capital ratio.
When all partners invest for the same duration, profit splits directly in the ratio of capitals. When durations differ, each partner’s effective contribution is capital × time (their "capital-months"), and profit is shared in the ratio of these products — this accounts for a partner who invested more money for less time versus one who invested less money for longer. Once the capital-time ratio is found, apply the common-multiplier technique from ratio-and-proportion to split the actual profit figure.
- One capital×time rule handles equal and unequal durations
- Reuses the ratio common-multiplier technique
- Extends cleanly to more than two partners
AI Mentor Explanation
Two batters share a partnership’s praise not just by runs scored but by balls faced too — a batter scoring 60 off 30 balls contributed a higher "rate" than one scoring 60 off 90 balls. Partnership problems weigh contribution the same way: it is not just capital invested but capital times duration, so a partner who invests more money for less time is compared fairly against one who invests less for longer via the capital × time product.
Worked example (unequal capital and time)
A
- 4000 × 6 = 24,000 capital-months
B
- 6000 × 4 = 24,000 capital-months
Ratio
- 24,000 : 24,000 = 1 : 1
Profit split (10,000 total)
- 5,000 to A, 5,000 to B
Step-by-Step Explanation
Step 1
Check durations
If all partners invested for the same time, use capital ratio directly.
Step 2
Compute capital × time
For unequal durations, multiply each partner’s capital by their months/years invested.
Step 3
Form the ratio
Express the capital-time products as a ratio, reduced to lowest terms.
Step 4
Split the profit
Use the common-multiplier technique to divide the total profit in that ratio.
What Interviewer Expects
- Recognition that time matters, not just capital
- Correct capital × time computation per partner
- Reuse of the ratio common-multiplier technique
- Handling partners joining/leaving partway through
Common Mistakes
- Splitting profit by capital alone when durations differ
- Forgetting to convert all durations to the same unit (months vs years)
- Mishandling a partner who joins or exits partway through the period
- Not reducing the capital-time ratio before applying it
Best Answer (HR Friendly)
“Profit isn’t split by capital alone — it’s split by capital multiplied by how long that capital was invested. So I calculate each partner’s capital times their duration, form that as a ratio, and then divide the actual profit figure using the same common-multiplier approach as any ratio problem.”
Follow-up Questions
- How do you handle a partner who joins the business after a few months?
- What if one partner’s capital changes partway through the year?
- How does this generalize to three or more partners?
- How is a working partner’s salary handled before profit is split?
MCQ Practice
1. A invests 5000 for 12 months, B invests 7500 for 8 months. What is the profit-sharing ratio?
A: 5000×12 = 60,000. B: 7500×8 = 60,000. Ratio = 60,000:60,000 = 1:1.
2. If all partners invest for the same duration, profit is split in the ratio of their?
When time is equal for all, it cancels out of the ratio, leaving capital as the only factor.
3. A and B invest 3000 and 5000 respectively for the same period. A profit of 8000 gives A a share of?
Ratio 3000:5000 = 3:5, total 8 parts. A gets 3/8 × 8000 = 3000.
Flash Cards
Core partnership rule? — Profit splits in the ratio of capital × time for each partner.
Equal durations? — Time cancels out; profit splits by capital ratio alone.
Capital-months? — A partner’s effective stake = capital invested × months invested.
How to split actual profit? — Use the common-multiplier ratio technique on the capital-time ratio.