Profit, Loss & Discount • Topic 6 of 6

Partnership in Trade

In a partnership, profit is shared in the ratio of each partner’s contribution, measured as capital × time invested. If A puts in ₹x for m months and B puts in ₹y for n months, profit is split in the ratio xm : yn. When all partners invest for the SAME duration, time cancels and the split is simply the ratio of capitals. CAT favours the unequal-time version, where someone joins late or withdraws early, so always multiply each capital by its own number of active months before forming the ratio. A "working partner" may also draw a salary or commission off the top first; subtract that, then divide the remaining profit by the capital-time ratio. The fast method is to compute each partner’s capital-month product, reduce to a clean ratio, and allocate the profit proportionally — no need to find individual investments unless asked.

✅ Solved examples

1. A invests ₹3,000 and B ₹2,000 for the same period. They earn ₹1,000 profit. Find each share.
Ratio 3000:2000 = 3:2. A = (3/5)·1000 = ₹600, B = ₹400.
2. A invests ₹6,000 for 12 months, B ₹8,000 for 6 months. Split a ₹3,300 profit.
Capital-months: A = 72,000, B = 48,000 ⇒ 72:48 = 3:2. A = ₹1,980, B = ₹1,320.
3. A starts with ₹5,000; after 4 months B joins with ₹6,000. At year end split ₹4,200.
A: 5000×12 = 60,000; B: 6000×8 = 48,000 ⇒ 60:48 = 5:4. A = (5/9)·4200 = ₹2,333.33, B = ₹1,866.67.
4. A and B invest ₹4,000 and ₹5,000. A is the working partner and takes 10% of profit as salary; the rest is split by capital. On ₹9,000 profit find A’s total.
Salary = 900. Remaining 8,100 split 4:5 ⇒ A gets (4/9)·8100 = 3,600. A total = 900 + 3,600 = ₹4,500.

✏️ Practice — try these, take hints as needed

1. A ₹4,000, B ₹6,000, same time, profit ₹2,500. B’s share?
Ratio 4:6 = 2:3.
B is 3 parts of 5.
(3/5)·2500.
₹1,500
2. A ₹2,000 for 6 months, B ₹3,000 for 4 months. Ratio of shares?
Multiply capital by months.
A = 12,000, B = 12,000.
Reduce.
1:1
3. A ₹10,000 for 12 mo, B ₹15,000 for 8 mo. Split ₹2,400.
A = 120,000, B = 120,000.
Ratio 1:1.
Half each.
₹1,200 each
4. A invests ₹8,000; B joins after 3 months with ₹12,000. Profit ₹5,400 at year end. B’s share?
A: 8000×12, B: 12000×9.
96,000 : 108,000 = 8:9.
B = (9/17)·5400.
₹2,858.82 (≈; 9/17 of 5400)
5. P, Q, R invest ₹5,000, ₹6,000, ₹4,000 for equal time. Profit ₹4,500. R’s share?
Ratio 5:6:4, total 15.
R is 4 parts.
(4/15)·4500.
₹1,200

📝 Topic test — 8 questions

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