Profit, Loss, and Discount: Master Guide

Basic Formulas

• Profit = SP - CP
• Loss = CP - SP
• Profit% = (Profit/CP) × 100
• Loss% = (Loss/CP) × 100
• SP = CP × (100 + Profit%)/100
• CP = SP × 100/(100 + Profit%)

Marked Price and Discount

• Discount = MP - SP
• Discount% = (Discount/MP) × 100
• SP = MP × (100 - Discount%)/100

Important Patterns

• If CP of x articles = SP of y articles, then Profit% = [(x-y)/y] × 100
• If profit is x% on CP, then profit on SP = [x/(100+x)] × 100%
• Successive discounts of a% and b% = Single discount of [a + b - ab/100]%

False Weights

• If seller uses weight w instead of 1000g, Profit% = [(1000-w)/w] × 100

Partnership

• Profit ratio = Capital ratio × Time ratio
• If A invests for t₁ months and B for t₂ months, ratio = (A×t₁):(B×t₂)

CAT Strategy

Mark-up and discount problems often have elegant ratio-based solutions.