Profit and Loss for SSC CGL - Complete Guide | CP, SP, Profit%, Loss%, Discount in Hindi

📌 Series Info: Chapter 2: Arithmetic
Post Number: 15/76 | Topic: 2.3 Profit & Loss
Previous: 2.2 Percentage ✅
Chapter 2 Progress: 3/20 topics

Introduction: Profit & Loss Kya Hai?

Namaste dosto! Aaj ham Profit & Loss (लाभ और हानि) padhenge. Ye SSC CGL me guaranteed 2-3 questions aate hain aur percentage ke concepts pe based hai.

Basic Terminology

🔹 Cost Price (CP) = क्रय मूल्य = Jis price pe kharida
🔹 Selling Price (SP) = विक्रय मूल्य = Jis price pe becha
🔹 Profit = लाभ = SP > CP (when you earn)
🔹 Loss = हानि = SP < CP (when you lose)

Example 1 (Profit):
Ek pen ₹50 me khareeda, ₹60 me becha
CP = ₹50, SP = ₹60
SP > CP, toh Profit hua
Profit = SP - CP = 60 - 50 = ₹10 ✓

Example 2 (Loss):
Ek book ₹100 me khareedi, ₹80 me bechi
CP = ₹100, SP = ₹80
SP < CP, toh Loss hua
Loss = CP - SP = 100 - 80 = ₹20 ✓

🎯 Exam Importance: SSC CGL me profit-loss questions:

Direct CP/SP calculations (2-3 questions)
Profit%/Loss% based problems
Marked Price & Discount combinations
Successive discounts
False weight/dishonest dealer problems
Partnership profit distribution

Basic Profit & Loss Formulas MUST KNOW

Profit Formulas

⭐ Profit = SP - CP ⭐
⭐ Profit% = (Profit/CP) × 100 ⭐
⭐ Profit% = [(SP - CP)/CP] × 100 ⭐

Example:
CP = ₹500, SP = ₹600
Profit = 600 - 500 = ₹100
Profit% = (100/500) × 100 = 20% ✓

Loss Formulas

⭐ Loss = CP - SP ⭐
⭐ Loss% = (Loss/CP) × 100 ⭐
⭐ Loss% = [(CP - SP)/CP] × 100 ⭐

Example:
CP = ₹800, SP = ₹720
Loss = 800 - 720 = ₹80
Loss% = (80/800) × 100 = 10% ✓

SP aur CP Find Karne Ke Formulas

When Profit% Given

SP nikalna: SP = CP × [(100 + Profit%)/100]
CP nikalna: CP = [SP × 100]/(100 + Profit%)

Example 1: CP = ₹400, Profit% = 25%. SP kya hoga?
SP = 400 × [(100 + 25)/100]
SP = 400 × 1.25 = ₹500 ✓

Example 2: SP = ₹1200, Profit% = 20%. CP kya thi?
CP = (1200 × 100)/(100 + 20)
CP = 120000/120 = ₹1000 ✓

When Loss% Given

SP nikalna: SP = CP × [(100 - Loss%)/100]
CP nikalna: CP = [SP × 100]/(100 - Loss%)

Example 1: CP = ₹600, Loss% = 10%. SP kya hoga?
SP = 600 × [(100 - 10)/100]
SP = 600 × 0.9 = ₹540 ✓

Example 2: SP = ₹450, Loss% = 10%. CP kya thi?
CP = (450 × 100)/(100 - 10)
CP = 45000/90 = ₹500 ✓

Marked Price & Discount IMPORTANT

Terminology

🔹 Marked Price (MP) = अंकित मूल्य = Price tag pe likha price
🔹 Discount = छूट = MP se kitna kam
🔹 Selling Price (SP) = MP - Discount

Discount Formulas

⭐ Discount = MP - SP ⭐
⭐ Discount% = (Discount/MP) × 100 ⭐
⭐ SP = MP × [(100 - Discount%)/100] ⭐

Example:
MP = ₹1000, Discount = 20%. SP kya hoga?
SP = 1000 × [(100 - 20)/100]
SP = 1000 × 0.8 = ₹800 ✓

Combined: MP, Discount, CP, Profit

Example:
Ek shopkeeper ne article ₹500 me khareeda. Usne MP ₹800 rakha aur 10% discount diya. Profit% kya hai?

Step 1: SP nikalo
SP = 800 × 0.9 = ₹720

Step 2: Profit nikalo
Profit = SP - CP = 720 - 500 = ₹220

Step 3: Profit%
Profit% = (220/500) × 100 = 44% ✓

Successive Discounts (क्रमागत छूट)

⭐ Agar do successive discounts x% aur y% hain:
Single Equivalent Discount = x + y - (xy/100) ⭐

Example 1:
MP = ₹2000 pe pehle 20% discount, phir 10% discount. Final SP?

Method 1 (Formula):
Equivalent discount = 20 + 10 - (20×10)/100
= 30 - 2 = 28%
SP = 2000 × 0.72 = ₹1440 ✓

Method 2 (Step by step):
After 1st discount: 2000 × 0.8 = ₹1600
After 2nd discount: 1600 × 0.9 = ₹1440 ✓

Example 2:
Teen successive discounts 10%, 20%, 30%. Single equivalent discount?

Step 1: Pehle do combine karo
10 + 20 - (10×20)/100 = 28%

Step 2: Ab 28% aur 30% combine
28 + 30 - (28×30)/100
= 58 - 8.4 = 49.6% ✓

Special Cases & Tricky Problems

Case 1: Equal Profit% aur Loss%

Important Rule:
Agar do items ko same % pe ek profit aur ek loss pe becha jaye:
Overall hamesha Loss hoti hai!
Loss% = (Common %)²/100

Example:
Do articles ko ₹500 each pe becha. Ek pe 20% profit, dusre pe 20% loss. Overall profit/loss?

Quick Formula:
Loss% = (20)²/100 = 400/100 = 4% loss ✓

Verification:
Article 1: SP = 500, Profit 20% → CP = 500/1.2 = ₹416.67
Article 2: SP = 500, Loss 20% → CP = 500/0.8 = ₹625
Total CP = 416.67 + 625 = ₹1041.67
Total SP = 500 + 500 = ₹1000
Loss = 1041.67 - 1000 = ₹41.67
Loss% = (41.67/1041.67) × 100 ≈ 4% ✓

Case 2: False Weight/Dishonest Dealer

Agar dealer 1000g ke bajaye x grams deta hai:
Profit% = [(1000 - x)/x] × 100

Example:
Ek shopkeeper 1 kg ke bajaye 900g deta hai but 1 kg ka price leta hai. Uski profit%?

Profit% = [(1000 - 900)/900] × 100
= (100/900) × 100
= 11.11% ✓

Case 3: Break-even (No Profit No Loss)

Jab SP = CP, toh no profit no loss
Profit% = 0%, Loss% = 0%

Quick Reference Formulas Table

Situation	Formula
Profit	SP - CP
Loss	CP - SP
Profit%	(Profit/CP) × 100
Loss%	(Loss/CP) × 100
SP (when Profit%)	CP × [(100 + P%)/100]
SP (when Loss%)	CP × [(100 - L%)/100]
CP (when Profit%)	[SP × 100]/(100 + P%)
CP (when Loss%)	[SP × 100]/(100 - L%)
Discount	MP - SP
SP (after discount)	MP × [(100 - D%)/100]
Successive Discount	x + y - (xy/100)

SSC CGL Level Practice Questions

Q1. Ek article ₹750 me khareeda aur ₹900 me becha. Profit% kya hai?
(A) 15%
(B) 18%
(C) 20%
(D) 25%

Answer: (C) 20%
Solution:
Profit = 900 - 750 = ₹150
Profit% = (150/750) × 100 = 20% ✓

Q2. Agar CP = ₹600 aur 25% profit chahiye, toh SP kya hona chahiye?
(A) ₹700
(B) ₹725
(C) ₹750
(D) ₹800

Answer: (C) ₹750
Solution:
SP = 600 × [(100 + 25)/100]
SP = 600 × 1.25 = ₹750 ✓

Q3. MP ₹2000 pe 20% aur 10% successive discounts. Final SP?
(A) ₹1400
(B) ₹1420
(C) ₹1440
(D) ₹1460

Answer: (C) ₹1440
Solution:
Equivalent discount = 20 + 10 - (20×10)/100 = 28%
SP = 2000 × 0.72 = ₹1440 ✓

Q4. Do items ko ₹1000 each pe becha. Ek pe 25% profit, dusre pe 25% loss. Overall profit/loss?
(A) No profit no loss
(B) 6.25% profit
(C) 6.25% loss
(D) 5% loss

Answer: (C) 6.25% loss
Solution:
Loss% = (25)²/100 = 625/100 = 6.25% ✓

Q5. Ek dealer 1kg ke bajaye 800g deta hai. Uski profit% kya hai?
(A) 20%
(B) 25%
(C) 30%
(D) 33.33%

Answer: (B) 25%
Solution:
Profit% = [(1000 - 800)/800] × 100
= (200/800) × 100 = 25% ✓

Exam Shortcuts & Quick Tricks

🚀 Trick 1: 10% Profit/Loss Quick
10% profit: SP = CP × 1.1 (multiply by 11, divide by 10)
10% loss: SP = CP × 0.9 (multiply by 9, divide by 10)

🚀 Trick 2: 20% Profit Quick
20% = 1/5
CP = 5 parts → SP = 6 parts
Example: CP = ₹500 → SP = ₹600

🚀 Trick 3: 25% Profit/Loss
25% = 1/4
Profit: CP = 4 parts → SP = 5 parts
Loss: CP = 4 parts → SP = 3 parts

🚀 Trick 4: Successive Discount Mental
10% + 10% = 19% (not 20%!)
20% + 20% = 36% (not 40%!)
25% + 25% = 43.75% (not 50%!)

Common Mistakes (ये गलतियां मत करना)

❌ Mistake 1: Profit/Loss% का base confuse करना
Wrong: SP के basis पर calculate करना ✗
Right: हमेशा CP के basis पर ✓

❌ Mistake 2: Successive discounts simply add करना
Wrong: 20% + 10% = 30% ✗
Right: Formula use करो = 28% ✓

❌ Mistake 3: Equal % profit aur loss = no profit no loss
Wrong: 20% profit + 20% loss = zero ✗
Right: Overall loss hoti hai = 4% ✓

❌ Mistake 4: Discount को CP मानना
Discount हमेशा MP से होता है, CP से नहीं!

Homework Practice (खुद Try करो)

CP = ₹850, SP = ₹1020. Profit% निकालो
Loss% = 15%, SP = ₹680. CP क्या थी?
MP = ₹1500 पे 25% discount. SP क्या होगी?
Successive discounts 30% और 20%. Single equivalent discount?
दो items ₹2400 each पे बेचे। एक पे 20% profit, दूसरे पे 20% loss। Overall profit/loss%?

Next Topic Preview

📚 अगले Post में: 2.4 Discount (छूट)
Advanced discount problems, markup price, profit after discount, multiple discount combinations और SSC level questions!

आज के profit-loss concepts directly apply होंगे!

Conclusion

Profit & Loss SSC CGL का high-scoring topic है। Formulas याद करो और practice करो। CP, SP, MP का confusion clear रखो। Percentage के साथ मिलकर ये topic हर paper में आता है!

Practice Strategy: Daily 20-25 profit-loss questions solve करो। Different types practice करो - basic calculations, successive discounts, dishonest dealer problems। Speed और accuracy दोनों improve करनी है!

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