🎙 Teacher-Style Introduction

Profit & Loss chapter real life se directly जुड़ा हुआ topic है – dukaan, business, discount, MRP, sab yahin se aata hai. Delhi Police Constable exam mein ye 2–3 super easy questions deta hai.

Agar aap CP (Cost Price), SP (Selling Price), Profit, Loss aur inka % relation samajh lenge, toh ye chapter हमेशा high-scoring rahega.

📘 Important Formulas / महत्वपूर्ण सूत्र

• Cost Price (CP) = buying price
• Selling Price (SP) = selling price
• Profit = SP − CP
• Loss = CP − SP
• Profit% = (Profit / CP) × 100
• Loss% = (Loss / CP) × 100
• SP (at profit%) = CP × (1 + Profit%/100)
• SP (at loss%) = CP × (1 − Loss%/100)

• लागत मूल्य (CP) = जिस दाम पर सामान खरीदा जाए
• विक्रय मूल्य (SP) = जिस दाम पर सामान बेचा जाए
• लाभ = SP − CP
• हानि = CP − SP
• लाभ% = (लाभ / CP) × 100
• हानि% = (हानि / CP) × 100
• SP (लाभ%) = CP × (1 + लाभ%/100)
• SP (हानि%) = CP × (1 − हानि%/100)

⚡ Tricks & Shortcuts / ट्रिक्स व शॉर्टकट

• Profit / Loss हमेशा CP पर निकाला जाता है (SP पर नहीं).
• “Profit% diya ho aur CP diya ho” → SP = CP × (100 + P)% / 100.
• “Loss% diya ho aur CP diya ho” → SP = CP × (100 − L)% / 100.
• Question mein “sold at 20% profit” likha ho → iska matlab SP = 120% of CP.
• DP exam mein numbers हमेशा छोटे aur आसान होते हैं (100, 150, 200 type).

🎯 Exam Angle (Delhi Police)

• Har paper mein 2–3 questions P&L se aana common hai.
• Mostly direct CP–SP–Profit%–Loss% based questions.
• No tricky shopkeeper cheating type questions – बस 1–2 step calculation.

✔ Solved Examples / हल प्रश्न

Example 1: A shopkeeper buys an item for ₹100 and sells it for ₹120. Find profit and profit%.
Solution (English): Profit = 120 − 100 = ₹20. Profit% = (20/100)×100 = 20%.
समाधान (Hindi): लाभ = 120 − 100 = ₹20, लाभ% = (20/100)×100 = 20%।

Example 2: An article is sold at 10% loss for ₹180. Find the cost price.
Solution: Let CP = x.
10% loss ⇒ SP = 90% of CP ⇒ 0.9x = 180 ⇒ x = 180 / 0.9 = ₹200.
समाधान: मान लें CP = x, 10% हानि पर SP = 90% of CP ⇒ 0.9x = 180 ⇒ x = 200।

Example 3: Find SP if CP = ₹250 and profit% = 12%.
Solution: Profit = 12% of 250 = 0.12 × 250 = 30 ⇒ SP = 250 + 30 = ₹280.

Example 4: A toy costs ₹400 and is sold at 15% loss. Find selling price.
Solution: Loss = 15% of 400 = 0.15 × 400 = 60 ⇒ SP = 400 − 60 = ₹340.

Example 5: If CP = ₹500 and SP = ₹475, find loss%.
Solution: Loss = 500 − 475 = 25.
Loss% = (25/500)×100 = 5%.

Example 6: An article is sold for ₹330 at 10% profit. Find CP.
Solution: 10% profit ⇒ SP = 110% of CP ⇒ 1.1×CP = 330 ⇒ CP = 330 / 1.1 = ₹300.

Example 7: If loss% is 20% and SP = ₹240, find CP.
Solution: 20% loss ⇒ SP = 80% of CP ⇒ 0.8×CP = 240 ⇒ CP = 240 / 0.8 = ₹300.

Example 8: CP = ₹600, loss = ₹30. Find loss%.
Solution: Loss% = (30/600)×100 = 5%.

✔ MCQs (Delhi Police Pattern)

1. CP = ₹200, SP = ₹240. Profit% = ?
   Answer: Profit = 40 → (40/200)×100 = 20%
2. CP = ₹150, loss% = 10%. SP = ?
   Answer: SP = 150 × (90/100) = ₹135
3. Loss of ₹25 on CP = ₹125. Loss% = ?
   Answer: (25/125)×100 = 20%
4. CP = ₹300, SP = ₹360. Profit% = ?
   Answer: Profit = 60 → (60/300)×100 = 20%
5. SP = ₹180 at 20% loss. CP = ?
   Answer: SP = 80% of CP ⇒ CP = 180 × (100/80) = ₹225
6. Profit of ₹40 at 8% profit. CP = ?
   Answer: 8% of CP = 40 ⇒ CP = 40 × (100/8) = ₹500
7. CP = ₹500, loss = ₹50. SP = ?
   Answer: SP = 500 − 50 = ₹450
8. SP = ₹264 at 10% profit. CP = ?
   Answer: SP = 110% of CP ⇒ CP = 264 × (100/110) = ₹240
9. If CP = ₹250, profit% = 5%. SP = ?
   Answer: SP = 250 × (105/100) = ₹262.50
10. CP = ₹800, loss% = 12.5%. Find SP.
    Answer: SP = 800 × (87.5/100) = 800 × 0.875 = ₹700

💡 Motivation: Aapne Profit & Loss jaise practical chapter ko master kar liya — ab shopkeeper ke hisaab se nahi, apne hisaab se sochoge. Ye hi officer wali soch hai. 🚓