Partnership • Topic 2 of 3

Profit Sharing

Once the investment ratio is fixed, sharing the profit is pure ratio arithmetic: each partner’s share = (their ratio term ÷ sum of terms) × total profit. The same rule shares a loss. CAT loves the reverse direction too — give you one partner’s profit and ask for total profit, or give the total and a difference between two shares. The fastest method is to find the "value of one part": divide a known share by its number of ratio units, then scale. For example, if the ratio is 3 : 4 : 5 and the largest share is ₹10,000, one part = 10000/5 = ₹2,000, so total profit = 12 parts = ₹24,000. A subtle but high-value trap: when partners invest for different times, never split profit by raw capital — first convert to capital-months, then share. Equal-profit questions invert this: if two partners earn equal profit, their capitals are in the inverse ratio of their time periods.

✅ Solved examples

1. A and B share profit in 5 : 7. If total profit is ₹36,000, find each share.
Parts = 12. One part = 36000/12 = ₹3,000. A = 5×3000 = ₹15,000; B = 7×3000 = ₹21,000.
2. A, B, C invest ₹20,000, ₹30,000, ₹50,000 for the same time. C’s share of profit is ₹15,000. Find total profit.
Ratio = 2 : 3 : 5 (parts 10). C = 5 parts = 15000 ⇒ one part = 3000 ⇒ total = 10×3000 = ₹30,000.
3. P invests ₹40,000 for 6 months, Q ₹30,000 for 8 months. Profit ₹26,000. Find Q’s share.
Capital-months: P = 2,40,000; Q = 2,40,000 ⇒ 1 : 1. Q = ₹13,000.
4. Two partners earn equal profit. A invested for 4 months, B for 6 months. Find the ratio of their capitals.
Equal profit ⇒ capitals inverse to time = 6 : 4 = 3 : 2 (A : B).

✏️ Practice — try these, take hints as needed

1. Profit ₹48,000 shared in 3 : 5. Find the larger share.
Parts = 8.
One part = 6000.
Larger = 5 parts.
₹30,000
2. A : B : C profit ratio 4 : 5 : 6; A gets ₹8,000. Total profit?
A = 4 parts = 8000.
One part = 2000.
Total = 15 parts.
₹30,000
3. X ₹25,000 for 12 months, Y ₹50,000 for 6 months. Profit ₹40,000. Y’s share?
Capital-months each.
3,00,000 : 3,00,000.
Ratio 1 : 1.
₹20,000
4. A and B get profit in 7 : 5. A gets ₹2,400 more than B. Total profit?
Difference = 2 parts.
2 parts = 2400.
Total = 12 parts.
₹14,400
5. Two partners earn equal profit; A invested ₹36,000, B ₹48,000. Ratio of their time periods?
Equal profit ⇒ time inverse to capital.
Time A : B = 48000 : 36000.
Cancel by 12,000.
4 : 3

📝 Topic test — 8 questions

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