Ratio, Proportion & Partnership • Topic 4 of 4

Partnership & Profit Sharing

In a partnership, profit divides in the ratio of each partner's contribution to the business = capital x time invested. If everyone invests for the same period, profit divides simply in the ratio of capitals. A working partner may take an extra salary or commission off the top before the remaining profit is shared. Always reduce each partner to a single capital-months figure first.

✅ Solved examples

1. A invests 5000 for 12 months, B invests 6000 for 8 months. A profit of 1800 is earned — find each share.
Ratio = 5000 x 12 : 6000 x 8 = 60000 : 48000 = 5:4 (9 parts). A = 5/9 x 1800 = 1000, B = 4/9 x 1800 = 800.
2. A and B invest 8000 and 12000 for the same time. Divide a profit of 5000.
Ratio 8:12 = 2:3 -> 5 parts. A = 2000, B = 3000.
3. A starts with 30000; after 4 months B joins with 45000. Year-end profit ratio?
A: 30000 x 12 = 360000; B: 45000 x 8 = 360000 -> ratio 1:1.
4. Three partners invest in ratio 3:4:5 for equal time. Profit 24000 — largest share?
12 parts; largest 5/12 x 24000 = 10000.

✏️ Practice — try these, take hints as needed

1. A 4000/12m, B 6000/12m. Divide 5000.
Same time -> 4:6 = 2:3.
5 parts.
—
A 2000, B 3000
2. A 10000/6m, B 5000/12m. Profit ratio?
60000 : 60000.
—
—
1:1
3. Ratio of capitals 2:3:5, same time, profit 30000. Smallest share?
10 parts.
2/10 x 30000.
—
6000
4. A 8000/12m, B 12000/6m. Ratio?
96000 : 72000.
Divide by 24000.
—
4:3
5. A invests for 12m, B (same amount) for 8m. Ratio?
Same capital.
12:8.
—
3:2

📝 Topic test — 8 questions

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