Percentages & Fraction Equivalents

Percentages are the bedrock of quantitative aptitude. Mastery of fractional conversions (e.g., 1/7 = 14.28%, 1/8 = 12.5%, 1/12 = 8.33%) enables calculating complex calculations mentally without scratchpad time loss.

Exam Frequency: 3 to 5 questions in TCS NQT, Infosys, and Bank PO Prelims

Essential Formulas & Shortcut Rules

Percentage Change = [(Final - Initial) / Initial] × 100

Always divide by the original or initial base quantity.

Net Change = a + b + (a × b)/100

Successive percentage changes of a% and b% (use negative signs for discounts or reductions).

Expenditure Balance: If Price rises by R%, Consumption must decrease by [R / (100 + R)] × 100

Keeps total expenditure constant when prices fluctuate.

Worked Step-by-Step Examples

Example 1: If the price of petrol increases by 25%, by what percentage should a driver reduce fuel consumption so that expenditure remains unchanged?

Step-by-Step Mathematical Derivation:

•Let original price = ₹100, original consumption = 100 units. Original expenditure = ₹10,000.

•New price = ₹125. New expenditure must remain ₹10,000.

•New consumption = 10,000 / 125 = 80 units.

•Reduction in consumption = 100 - 80 = 20 units.

•Alternative Shortcut: [R / (100 + R)] × 100 = [25 / 125] × 100 = (1/5) × 100 = 20%.

Answer: 20% reduction

💡 Speed Shortcut: Whenever price increases by 1/n, consumption must decrease by 1/(n + 1) to keep product invariant.

Example 2: A jacket is priced at ₹2,000. It undergoes a discount of 20% followed by an additional festive cashback discount of 10%. What is the effective single discount percentage and final price?

Step-by-Step Mathematical Derivation:

•Net discount using successive formula: a = -20, b = -10.

•Net = -20 + (-10) + [(-20 × -10) / 100] = -30 + 2 = -28%.

•Effective single discount = 28%.

•Final price = 2000 × (1 - 0.28) = 2000 × 0.72 = ₹1,440.

Answer: 28% effective discount; ₹1,440 final price

💡 Speed Shortcut: Never simply add percentage discounts (20% + 10% ≠ 30%). The second discount applies to the discounted subtotal.

Common Exam Traps to Avoid

✕Confusing "A is what percentage of B" ([A/B] × 100) with "A is what percentage more than B" ([(A - B)/B] × 100).
✕Applying percentage increases directly to selling price instead of cost price.
✕Ignoring that successive percentage changes are commutative: a 10% increase followed by a 20% increase yields the exact same result as a 20% increase followed by a 10% increase.

Interactive Practice Drill (4 Questions)

Instant Explanations • Timed

Assessment Simulator

Percentages & Fraction Equivalents Practice Drill

4 Questions • No negative marking

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1Percentages & Fraction Equivalents

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A laptop originally priced at ₹50,000 has its price increased by 20% during festival season. After the festival, the new price is discounted by 20%. What is the final price of the laptop?

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