SSC GD · Bite-size lessons

Percentage

About 6 min · Elementary Mathematics · English

Time worked out from the lesson's 441 words at 150 words a minute, plus a minute for each question.

Percentage is a core topic in the SSC GD Elementary Mathematics section. The word "per cent" literally means "per hundred" or "out of 100", making it a standardised way to compare fractions and express proportions.

Key ideas

• Definition: x% means x/100. To convert a percentage to a fraction or decimal, divide by 100. To convert a fraction or decimal to percentage, multiply by 100.
• Base Value: The quantity on which percentage is calculated is called the base or reference value. "20% of 500" means base = 500. Always identify the base correctly.
• Percentage Increase/Decrease: If a value V increases by r%, the new value = V × (1 + r/100). If it decreases by r%, new value = V × (1 - r/100).
• Percentage Change Formula: Percentage change = [(New Value - Original Value) / Original Value] × 100. Positive result = increase, negative = decrease.
• Successive Percentage Changes: When two percentage changes happen one after another, you cannot simply add them. Use the formula: Net effect = a + b + (ab/100), where a and b are the two percentage changes (use negative sign for decrease).

Watch out for

• Adding successive percentages directly → Wrong: 10% increase + 10% decrease = 0% change. Correct: Use formula a + b + ab/100 or calculate step-by-step. The base changes after first operation.
• Confusing base value → Wrong: "A is 20% more than B" does NOT mean "B is 20% less than A". Correct: If A = B × 1.2, then B = A/1.2 = A × (100/120) = 83.33% of A, meaning B is 16.67% less than A.
• Calculation errors with decimals → Wrong: 12.5% of 80 = 12.5 × 80 = 1000. Correct: Remember to divide by 100: (12.5/100) × 80 = 10.

Quick reference

• 1% shortcut: To find 1% of any number, divide by 100 (shift decimal two places left). Then multiply for other percentages.
• 50% = half, 25% = quarter, 10% = one-tenth — use these to split calculations mentally.
• Increase + Decrease of same %: Always results in a net decrease. For r% each, net decrease = r²/100%.
• Common conversions: 1/8 = 12.5%, 1/6 = 16.67%, 1/3 = 33.33%, 2/3 = 66.67%.
• Reverse formula memory: After r% increase → divide by (1 + r/100); after r% decrease → divide by (1 - r/100).

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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