Percentages: Shortcuts and Formulas

Successive Percentage Change

If a value changes by a% then b%, net change = a + b + (ab/100)

Example: +20% then -25%

Net = 20 - 25 + (20×-25)/100 = -10%

Percentage to Fraction Conversions

• 10% = 1/10
• 12.5% = 1/8
• 16.67% = 1/6
• 20% = 1/5
• 25% = 1/4
• 33.33% = 1/3
• 50% = 1/2
• 66.67% = 2/3
• 75% = 3/4

Profit and Loss

• Profit% = (Profit/CP) × 100
• SP = CP × (100 + Profit%)/100
• If SP = CP, Profit% = 0
• Discount% = (Discount/MP) × 100

Common Patterns

• If price increases by x%, consumption must decrease by [x/(100+x)] × 100% to keep expenditure same
• Two successive discounts of a% and b% = Single discount of [a + b - ab/100]%

CAT Strategy

Memorize fraction equivalents - saves 20-30 seconds per question.