🎙 Teacher-Style Introduction

Partnership chapter व्यवसाय में profit sharing पर आधारित है—कौन कितना पैसा लगाता है और कितना समय तक लगाता है, उसी के अनुसार लाभ का बँटवारा होता है। Delhi Police exam में partnership के 1–2 direct और आसान सवाल आते हैं।

📘 Important Formulas / महत्वपूर्ण सूत्र

🔹 Basic Formula

If A invests A₁ for T₁ months and B invests A₂ for T₂ months:
Profit Ratio = (A₁ × T₁) : (A₂ × T₂)

🔹 When more than 2 partners

A : B : C = (A₁ × T₁) : (A₂ × T₂) : (A₃ × T₃)

🔹 Important Note

• Time must be in same unit (usually months).
• If time same → ratio = investment ratio.
• Profit हमेशा investment × time पर depends करता है।

⚡ Tricks & Shortcuts

• “Investment × Time” को directly multiply कर दो—यही final ratio है।
• Late entry/early exit → बस वास्तविक समय use करो।
• Common factor simplify करके ratio सरल बनाओ।
• DP exam में hardly 2-step calculation होती है।

✔ Solved Examples / हल प्रश्न

Example 1: A invests 2000 for 12 months, B invests 3000 for 12 months.
Ratio = 2000×12 : 3000×12 = 2000 : 3000 = 2 : 3

Example 2: A invests 4000 for 6 months, B invests 2000 for 12 months.
A = 4000×6 = 24000
B = 2000×12 = 24000
Ratio = 1 : 1

Example 3: A invests 3000 for 8 months, B invests 6000 for 4 months.
A = 24000
B = 24000
Ratio = 1 : 1

Example 4: A invests 5000 for 3 months, B invests 3000 for 9 months.
A = 15000
B = 27000
Ratio = 15 : 27 = 5 : 9

Example 5: A invests 6000 for 12 months, B invests 9000 for 6 months.
A = 72000
B = 54000
Ratio = 72 : 54 = 4 : 3

Example 6 (3 partners): A invests 2000 for 12 months B invests 3000 for 8 months C invests 4000 for 6 months
A = 24000, B = 24000, C = 24000
Ratio = 1 : 1 : 1

Example 7: Profit = ₹6000, A:B = 3:2 A = 3600, B = 2400.

Example 8: B enters after 3 months. A = 5000×12 = 60000 B = 3000×9 = 27000 Ratio = 60000 : 27000 = 20 : 9

✔ MCQs (Delhi Police Pattern)

1. A:2000 for 12 months, B:3000 for 12 months → Ratio? Ans: 2 : 3
2. A:3000(6m), B:2000(12m) → Ratio? Ans: 3 : 4
3. A:4000(12m), B:4000(6m) → Ratio? Ans: 2 : 1
4. A:B = 3:5, profit = 16000. A’s share? Ans: 6000
5. A invests 2500 for 10 months, B invests 5000 for 5 months. Ratio = 1 : 1
6. A:5000(12m), B:3000(4m) → 5000×12 = 60000 3000×4 = 12000 Ratio = 5 : 1
7. Total profit 9000, ratio 4:2:1 → B’s share? Ans: 2571.42
8. Success ratio: A enters late by 2 months. A=4000(10m), B=3000(12m).
   A=40000, B=36000 → 10 : 9
9. Ratio of 6000(3m) and 2000(9m) =
   18000 : 18000 = 1 : 1
10. If A gets 3000 out of 12000 profit, find ratio A:Total. Ans: 1 : 4

💡 Motivation: Partnership सिखाता है — अकेले नहीं, मिलकर बड़ी जीत मिलती है। Officer बनने की तैयारी भी teamwork से ही होती है! 🚓🔥