SSC Notes / Quantitative Aptitude / Chapter 6
Chapter 6 of 27

Percentage

Percentage-fraction conversions, successive percentage change, and the population/consumption-adjustment question patterns that build on them.

📖 ~13 min read 🔢 SSC Quantitative Aptitude

Introduction

Percentage is the single most foundational chapter for the entire "commercial arithmetic" cluster — Profit-Loss, Simple/Compound Interest, and Data Interpretation all reduce to percentage calculations at their core.

Base Concept

Percentage = (Value ÷ Total) × 100. Use the fraction table from Chapter 2 to convert common percentages instantly instead of calculating from scratch.

Percentage Increase/Decrease

FormulaUse
New Value = Original × (100 + %change)/100For a percentage increase
New Value = Original × (100 − %change)/100For a percentage decrease

Successive Percentage Change Formula

Flowchart — Net Effect of Two Successive Changes
Net % Change = a + b + (ab/100)

Use "+a" for an increase and "−a" for a decrease. This single formula replaces two-step calculations for any successive percentage change question.

Q. A number is increased by 20% and then decreased by 10%. Find the net percentage change.
Net change = 20 + (−10) + (20 × −10)/100 = 10 − 2 = +8% (net increase)

Population Growth / Decline (Compound-style)

SituationFormula
Population increases every year by r%Population after n years = P × (1 + r/100)ⁿ
Population decreases every year by r%Population after n years = P × (1 − r/100)ⁿ
Q. The population of a town is 10,000. It increases by 10% each year. Find the population after 2 years.
10,000 × (1.1)² = 10,000 × 1.21 = 12,100

"If A is x% more than B" Pattern

Flowchart — Reverse Percentage Relationship
If A is x% more than B → B is [x/(100+x)]×100 % less than A
Q. A's salary is 25% more than B's. By what % is B's salary less than A's?
B is less than A by [25/(100+25)] × 100 = [25/125] × 100 = 20%

Expenditure-Consumption Trade-off

A very common SSC pattern: "If the price of a commodity increases by x%, by what % should consumption decrease to keep expenditure unchanged?"

Formula
Required % decrease in consumption = [x/(100+x)] × 100
Q. The price of sugar increases by 25%. By what % must a family reduce consumption to keep expenditure the same?
Required decrease = [25/(100+25)] × 100 = 20%
💡 Exam Tip: The "x/(100+x)" and "x/(100−x)" reverse-percentage patterns appear disguised in salary comparison, price-consumption, and even Time-Speed-Distance questions — recognising the pattern instantly is worth more than re-deriving it each time.
✅ Practice Focus: Successive % change formula (a+b+ab/100) · Population growth/decline compound formula · Reverse percentage (A more than B → B less than A) · Price-consumption trade-off pattern.

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