Introduction
Partnership questions ask how profit (or loss) should be divided among business partners — a direct
application of the Ratio & Proportion concepts from Chapter 7, with the added twist of accounting for
different investment durations.
Simple Partnership
When all partners invest for the same time period, profit is divided in the ratio of their investments.
Q. A and B invest ₹5,000 and ₹8,000 respectively in a business for one year. If the profit is ₹5,200, find each partner's share.
Ratio of investment = 5000:8000 = 5:8
A's share = (5/13) × 5200 = ₹2,000
B's share = (8/13) × 5200 = ₹3,200
Compound Partnership
When partners invest different amounts for different time periods, profit is divided in the ratio of (Investment × Time) for each partner.
Flowchart — Compound Partnership Rule
Profit Share Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂) : ...
Q. A invests ₹4,000 for 6 months and B invests ₹6,000 for 4 months. If the total profit is ₹2,300, find each one's share.
A's capital-time = 4000×6 = 24,000
B's capital-time = 6000×4 = 24,000
Ratio = 24000:24000 = 1:1
Each partner's share = ₹1,150
Partner Joins Later / Leaves Early
Q. A starts a business with ₹5,000. After 4 months, B joins with ₹8,000. If the annual profit is ₹9,300, find each one's share.
A invests for the full 12 months, B invests for (12−4) = 8 months
A's capital-time = 5000×12 = 60,000
B's capital-time = 8000×8 = 64,000
Ratio = 60000:64000 = 15:16
A's share = (15/31)×9300 = ₹4,500
B's share = (16/31)×9300 = ₹4,800
Working Partner Pattern
⚠️ Common Trap: If a question mentions a "working partner" who receives extra compensation (a fixed salary or commission) for managing the business, that amount must be deducted from the total profit first before dividing the remainder in the capital-time ratio.
✅ Practice Focus: Simple partnership (investment ratio only) vs compound partnership (investment × time ratio) · Adjusting time for partners who join late or leave early · Working-partner salary deduction before ratio division.