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.
Kharida → becha: profit kahan se aaya?
Formula: Profit = SP − CP. Profit hamesha CP (kharid) par nikalta hai — MRP par nahi.
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!
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 — 100Marked 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.
MRP 1999 pe pehle 30% off, phir extra 10% off. Kitne me milega? Successive discount — seedha formula.
Pehla: 1999 x 0.70 = 1399.3
Dusra: 1399.3 x 0.90 = 1259.4
Trick: 0.70 x 0.90 = 0.63, matlab 37% total off.
Ans: Rs.1259- 4-6Q aptitude me — profit hamesha CP pe, MRP pe nahi. Yehi sabse bada trap.
- 45-sec target: pehle 10% nikaalo, phir multiply karo.
Profit-loss aur discount samajh aa gaya? Ab Time, Speed & Distance seekhte hain — formulas tricky hain but shortcuts se easy ho jaayega.