Lesson 3 � Intermediate

Profit, Loss & Discount

Profit-loss har exam mein aata hai. Percentages pe based hai but thoda alag soch chahiye. CP, SP, MP, discount � sab ek saath kaise handle karein✓ Chalo shortcuts ke saath seekhte hain.

? 22 min✓ Intermediate✓ Percentages basics

Profit & Loss basics

WHAT

CP = Cost Price (tumne kitne mein kharida), SP = Selling Price (tumne kitne mein becha). Agar SP > CP toh profit, agar SP < CP toh loss. Profit = SP - CP, Loss = CP - SP.

WHEN

Shopkeeper, business, discount offers, marked price � sab mein profit-loss concept use hota hai. MNC exams mein ye 4-6 questions aate hain har baar.

WHERE

Percentage pe based hai � agar percentages strong hai toh ye easy hai. Important: Profit/Loss hamesha CP pe calculate hota hai, SP pe nahi!

Golden Rule: Profit ya Loss hamesha CP (Cost Price) pe calculate hota hai, SP pe nahi. % Profit = (Profit/CP) � 100. Ye sabse common mistake hai � SP pe calculate karna.

Important formulas

# Basic formulas:
# Profit = SP - CP
# Loss = CP - SP
# Profit% = (Profit/CP) � 100
# Loss% = (Loss/CP) � 100

# Finding SP:
# If profit: SP = CP � (1 + Profit%/100)
# If loss: SP = CP � (1 - Loss%/100)

# Finding CP:
# If profit: CP = SP / (1 + Profit%/100)
# If loss: CP = SP / (1 - Loss%/100)

# Discount:
# MP = Marked Price (rate card pe likha hai)
# Discount = MP - SP
# Discount% = (Discount/MP) � 100
# SP = MP � (1 - Discount%/100)

Shortcut tricks

# Shortcut 1: CP find karna jab loss hai
# Agar item ko 10% loss pe ?450 mein becha
# CP = 450 / (1 - 10/100) = 450 / 0.9 = ?500
# Trick: Divide by (1 - loss%/100)

# Shortcut 2: Successive discounts
# 20% + 10% discount = NOT 30%!
# Effective discount = 20 + 10 - (20�10)/100 = 28%
# Same formula as successive percentage change

# Shortcut 3: Single discount equivalent
# Two discounts d1 and d2:
# Single equivalent = d1 + d2 - (d1�d2)/100

# Shortcut 4: Profit from false weight
# Shopkeeper 900g ke liye 1000g ka price leta hai
# Profit% = (1000-900)/900 � 100 = 22.22%
# Formula: (True weight - False weight)/False weight � 100

Pro Tip: Agar tumhe CP nikalna hai aur profit/loss% given hai, toh denominator mein (1 � %/100) use karo. Profit ke liye +, loss ke liye -. Ye formula exam mein fastest method hai.

Marked Price & Discount

Dukaan mein jo rate lagta hai wo MP hai. Usmein discount milta hai. Final jo pay karte ho wo SP hai:

# Relationship: MP ✓ discount ✓ SP ✓ profit/loss ✓ CP

# Example: MP = ?1000, 20% discount, 10% profit on CP
# SP = 1000 � (1 - 20/100) = ?800
# Now, SP = CP � (1 + 10/100)
# 800 = CP � 1.1
# CP = 800/1.1 = ?727.27

# Shortcut: When discount = profit%
# MP = CP � (100+P)/(100-D)
# If P = D, then MP = CP (no profit no loss)

# When there's NO discount but profit:
# Profit% = (MP - CP)/CP � 100

# When there's discount AND profit:
# MP � (1-D/100) = CP � (1+P/100)
# MP/CP = (100+P)/(100-D)

Exercise

Question: Ek cheez ?800 mein kharidi aur 50% profit pe becha. Selling price kitna hai✓ Sirf number daalo.

Question: Kisi cheez ko 20% loss pe ?400 mein becha. Cost price kitni thi✓ Sirf number daalo.

Question: Do successive discounts 20% aur 10% hain. Effective discount kitna hai? (Sirf number, bina % sign ke)

Question: MP = ?800 hai, 20% discount diya. SP kitna hoga✓ Sirf number daalo.

Common mistakes

Profit/Loss SP pe calculate karna: Hamesha CP pe calculate karo. Ye sabse common error hai.
Successive discounts direct add karna: 20% + 10% ? 30%. Formula use karo: a + b - ab/100.
"On" ka matlab samajhna: "Loss on SP" vs "Loss on CP" � confuse mat ho. Default CP hai.
False weight ka formula galat hona: Profit% = (True - False)/False � 100, nahi ki (True - False)/True � 100.

Lesson complete?

Profit-loss aur discount samajh aa gaya✓ Ab Time, Speed & Distance seekhte hain � formulas tricky hain but shortcuts se easy ho jaayega.