In this guide
In a typical SSC CGL paper, you may see only one or two questions labelled "percentage". But look closer at the profit and loss, discount, interest and data interpretation questions, and you'll find percentages inside almost all of them. That is why coaches often say: master percentages first, and half of arithmetic follows.
The core idea
"Percent" means per hundred. x% of a quantity = (x/100) × the quantity.
Fraction equivalents save time
| Percentage | Fraction |
|---|---|
| 10% | 1/10 |
| 12.5% | 1/8 |
| 16.67% | 1/6 |
| 20% | 1/5 |
| 25% | 1/4 |
| 33.33% | 1/3 |
| 37.5% | 3/8 |
| 62.5% | 5/8 |
| 66.67% | 2/3 |
| 83.33% | 5/6 |
Example: 37.5% of 640 = 3/8 × 640 = 240 — no long multiplication needed.
Percentage change
Percentage change = (change ÷ original) × 100.
The multiplier method
- An increase of r% means multiplying by (1 + r/100).
- A decrease of r% means multiplying by (1 − r/100).
Example: A price of ₹800 rises by 15%: 800 × 1.15 = ₹920.
Successive changes
Two successive changes of a% and b% give a net change of:
a + b + (ab/100) — using negative values for decreases.
Worked example: A salary increases by 20% and then decreases by 20%.
Net = 20 − 20 + (20 × −20)/100 = −4%. The salary falls by 4%.
For three or more changes, multiply the factors: 1.1 × 1.2 × 0.9 = 1.188, so a net increase of 18.8%.
"More than" and "less than"
If A is r% more than B, then B is [r/(100 + r)] × 100% less than A.
Worked example: A's salary is 25% more than B's. By what percentage is B's salary less than A's?
25/125 × 100 = 20%.
If A is r% less than B, then B is [r/(100 − r)] × 100% more than A.
Price, consumption and expenditure
Expenditure = price × consumption. If the price rises by r%, the percentage by which consumption must fall to keep expenditure unchanged is:
[r/(100 + r)] × 100%
Worked example: Sugar becomes 25% more expensive. By how much must a family cut consumption to spend the same?
25/125 × 100 = 20%.
Population and depreciation
- Population after n years = P × (1 + r/100)^n.
- Value after depreciation = V × (1 − r/100)^n.
Worked example: A town of 50,000 grows by 10% a year. Population after 2 years = 50,000 × 1.21 = 60,500.
Marks and elections
Worked example: In an election between two candidates, the winner gets 58% of the valid votes and wins by 2,400 votes. How many valid votes were cast?
The margin is 58% − 42% = 16% of the valid votes. 16% = 2,400, so 100% = 15,000.
Worked example: A student needs 40% to pass, scores 180 and fails by 20 marks. What are the maximum marks?
Pass mark = 200 = 40% of the total, so the total = 500.
Common traps
| Trap | Correct approach |
|---|---|
| Adding successive percentages directly | Use a + b + ab/100 |
| Using the wrong base | Always ask "percentage of what?" |
| Confusing percentage points with percent | A rise from 10% to 12% is 2 percentage points but a 20% increase |
Practice
- Find 62.5% of 480.
- A number is increased by 30% and then decreased by 30%. What is the net change?
- A is 20% less than B. By what percentage is B more than A?
- The price of petrol rises by 20%. By what percentage must consumption be reduced to keep expenditure the same?
- A machine worth ₹1,00,000 depreciates by 10% a year. What is its value after 2 years?
- In an exam, 35% is needed to pass. A student scored 210 and failed by 35 marks. Find the maximum marks.
Answers: 1. 300. 2. 9% decrease. 3. 25%. 4. 16.67%. 5. ₹81,000. 6. 700.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .
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