Introduction
Partnership questions split profit among two or more partners in proportion to their investment — and, when time
periods differ, in proportion to investment × time. This chapter is a direct application of
Ratio & Proportion.
Core Rule
Profit-sharing ratio = (Investment of A × Time of A) : (Investment of B × Time of B) : ...
If all partners invest for the same duration, the ratio simplifies to just the investment ratio.
Q. A and B invest ₹8,000 and ₹12,000 respectively in a business for the whole year. If the total profit is ₹15,000, find each partner's share.
Equal time, so profit ratio = investment ratio = 8000:12000 = 2:3. Total parts = 5.
A's share = (2/5) × 15000 = ₹6,000. B's share = (3/5) × 15000 = ₹9,000.
Q. A invests ₹10,000 for 12 months and B invests ₹15,000 for 8 months. Find their profit-sharing ratio.
Ratio = (10000×12) : (15000×8) = 120000 : 120000 = 1 : 1.
⚠️ Key Insight: If a partner joins later or leaves early, adjust their "time" to only the months
they were actually invested — this is where most partnership errors occur.
💡 Exam Tip: Working (or "sleeping" vs "active") partners sometimes get a fixed management fee
before the remaining profit is split by ratio — read the question carefully for this condition before applying
the standard ratio formula.
✅ Practice Focus: Equal-time investment ratio · Investment×time ratio for unequal durations ·
Partner joining/leaving mid-year problems.