Partnership Basics

🎯 Learning Objective

Share profits in the ratio of capital × time for each partner.

💡 Concept

• Profit share is proportional to Capital × Time invested
• Same time for all → profit ratio = capital ratio
• Same capital for all → profit ratio = time ratio
• Profit ratio = C₁T₁ : C₂T₂ : C₃T₃ (time in months)
• Loss is shared in exactly the same ratio as profit

🧮 Key Formulas

Profit ratio = C₁T₁ : C₂T₂ : C₃T₃

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Share of A = Total profit × (A's part/sum of parts)

✏️ Easy Example

Q. A and B invest ₹20,000 and ₹30,000 in a shop. The profit after a year is ₹15,000. Find A's share.

1. Same time → ratio = 20000:30000 = 2:3
2. One part = 15000/5 = 3000
3. A = 2 × 3000

Answer: ₹6,000

🇮🇳 Real-Life Example

Two friends open a juice corner — one puts in ₹20,000, the other ₹30,000. Splitting profit 2:3 instead of 50-50 is what keeps the friendship alive.

📝 Exam-Level Example

Q. A, B and C invest ₹25,000, ₹35,000 and ₹40,000 in a business. The annual profit is ₹40,000. Find C's share.

1. Ratio = 25:35:40 = 5:7:8
2. Total parts = 20; one part = 40000/20 = 2000
3. C = 8 × 2000

Answer: ₹16,000

📝 Exam-Level Example

Q. A invests ₹12,000 for 8 months and B invests ₹16,000 for 6 months. Divide a profit of ₹6,000.

1. A = 12000 × 8 = 96000
2. B = 16000 × 6 = 96000
3. Ratio 1:1 → equal shares

Answer: ₹3,000 each

🪄 Memory Trick

Simplify capitals before multiplying by time — 25000:35000:40000 is just 5:7:8. Small numbers, fast answers.

⚠️ Common Mistakes

• ❌ Splitting profit by capital ratio when the time periods differ
• ❌ Dividing the profit equally because they are 'partners'
• ❌ Mixing months and years in the same ratio

🏆 Exam Tips

• ✅ Always convert every duration to months before multiplying
• ✅ Cancel common zeros in capitals first — the ratio is all that matters

📌 Summary

• Profit ∝ Capital × Time
• Same time → capital ratio; same capital → time ratio
• Loss splits in the same ratio too
• Simplify the ratio before dividing profit