Percentage

About 6 min · Quantitative Aptitude (Basic Arithmetic Skill) · English

Time worked out from the lesson's 392 words at 150 words a minute, plus a minute for each question.

Percentage is one of the most fundamental topics in SSC CHSL Tier 1 quantitative aptitude. Nearly every arithmetic sub-topic—profit and loss, simple and compound interest, ratio and proportion—builds upon percentage concepts.

Key ideas

Percentage means "per hundred": 45% = 45/100 = 0.45. It is a way of expressing a fraction with denominator 100.
Conversion is bidirectional: To convert a fraction to percentage, multiply by 100. To convert percentage to fraction, divide by 100 and simplify.
Percentage of a quantity: To find x% of N, compute (x/100) × N. This is the most common calculation in every problem.
Percentage increase/decrease: If a value changes from A to B, percentage change = [(B − A)/A] × 100. Positive means increase, negative means decrease.
Successive percentage changes do not add: If a value increases by 10% then decreases by 10%, the net effect is NOT zero. Use the formula: Net% = a + b + (ab/100) where a and b are the two percentage changes.

Watch out for

Successive percentages assumed additive → Wrong: 10% increase then 10% decrease = 0% change. Correct: Net = 10 + (−10) + (10 × −10)/100 = −1%. Always use the formula.
Confusing "x% more than" with "x% of" → Wrong: "A is 25% more than B" does NOT mean A = 25% of B. Correct: A = B + 25% of B = 1.25B.
Reversing percentage without adjusting the base → Wrong: If salary increased 20% to ₹6000, original = 6000 − 20% of 6000. Correct: Original = 6000/1.20 = 5000. The 20% was applied on the original, not the new amount.

Quick reference

50% = 1/2; 33⅓% = 1/3; 25% = 1/4; 20% = 1/5; 16⅔% = 1/6; 12.5% = 1/8
Percentage change = [(New − Old)/Old] × 100
Successive changes: Net = a + b + ab/100 (signs matter: increase +, decrease −)
To remove x% increase: Divide by (1 + x/100)
To remove x% decrease: Divide by (1 − x/100)

Check yourself: 3 questions

1. If a shopkeeper marks an article 25% above the cost price and then offers a discount of 10%, what is his profit percentage?
2. A number is increased by 25% and then decreased by 20%. What is the net percentage change in the number?
3. If 35% of a number is 140, what is 25% of the same number?

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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