Percentage Questions: Method and Worked Examples
Find the base first and the rest is multiplication. Six original questions, solved step by step.
Percent means "out of 100". So 35% of a number is 35/100 of it. Most percentage questions come back to one idea: find the base, the number you are taking the percentage of, and the rest is simple multiplication.
Percentage is also the language of data interpretation and most other arithmetic topics. Getting it fast and exact here makes many other questions easier.
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Types of Percentage Questions
Percentage of a number
What it asks
A share of a whole
Example wording
Find 37.5% of 640
Percentage change
What it asks
Rise or fall from an old value
Example wording
Price went from ₹40 to ₹46. Find the % increase
Comparison
What it asks
How much more or less one value is than another
Example wording
A earns 25% more than B. By what % does B earn less than A?
Successive change
What it asks
Two or more changes, one after another
Example wording
Population rises 10% then falls 5%
Consumption and spending
What it asks
Keeping spending the same when price changes
Example wording
Price rises 20%. How much should use fall?
Votes and marks
What it asks
Working back from a difference or a shortfall
Example wording
Winner won by 4,800 votes with 58% of the votes
| Type | What it asks | Example wording |
|---|---|---|
| Percentage of a number | A share of a whole | Find 37.5% of 640 |
| Percentage change | Rise or fall from an old value | Price went from ₹40 to ₹46. Find the % increase |
| Comparison | How much more or less one value is than another | A earns 25% more than B. By what % does B earn less than A? |
| Successive change | Two or more changes, one after another | Population rises 10% then falls 5% |
| Consumption and spending | Keeping spending the same when price changes | Price rises 20%. How much should use fall? |
| Votes and marks | Working back from a difference or a shortfall | Winner won by 4,800 votes with 58% of the votes |
The Method
- 1
1. Find the base
Ask: percent of what? In "A is 25% more than B", the base is B. In a change, the base is the old value.
- 2
2. Turn the percentage into a fraction or decimal
25% = 1/4, 12.5% = 1/8, 20% = 1/5, 37.5% = 3/8. Fractions are often faster than multiplying by 0.375.
- 3
3. For a change, use a multiplier
A 10% rise means multiply by 1.10. A 5% fall means multiply by 0.95. For two changes, multiply both multipliers.
- 4
4. For a working-back question, set the known amount equal to its percentage
If 16% of the total is 4,800, then 1% is 300 and 100% is 30,000.
Practice Questions With Full Solutions
Original questions written for this page. Try each one before reading the solution.
- 1
Practice question 1: Find 37.5% of 640.
37.5% = 3/8. 640 ÷ 8 = 80, and 80 × 3 = 240. Answer: 240.
- 2
Practice question 2: A town has 48,000 people. The population rises 10% in the first year and falls 5% in the second. What is it after two years?
After year 1: 48,000 × 1.10 = 52,800. After year 2: 52,800 × 0.95 = 50,160. Answer: 50,160. The net change is 4.5%, not 10 − 5 = 5%.
- 3
Practice question 3: A earns 25% more than B. By what percentage does B earn less than A?
Let B = 100. Then A = 125. The difference is 25, but now the base is A. 25 ÷ 125 × 100 = 20%. Answer: 20%.
- 4
Practice question 4: The price of sugar rises 20%. By what percentage must a family cut its sugar use to spend the same amount?
Let the old price be 100 for 100 units of use. The new price is 120. With the same spend of 100, use = 100 ÷ 120 × 100 = 83⅓ units. The cut is 100 − 83⅓ = 16⅔%. Answer: 16⅔%.
- 5
Practice question 5: In a two-candidate election, the winner got 58% of the valid votes and won by 4,800 votes. How many valid votes were cast?
The loser got 42%. The gap is 58% − 42% = 16%. So 16% = 4,800, 1% = 300, and 100% = 30,000. Check: 58% is 17,400, 42% is 12,600, and the gap is 4,800. Answer: 30,000.
- 6
Practice question 6: A student needs 40% to pass. She scores 172 marks and fails by 28. What are the maximum marks?
Pass mark = 172 + 28 = 200. So 40% = 200, 1% = 5, and 100% = 500. Answer: 500.
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Common Traps
- check_circleUsing the wrong base. "25% more than B" and "20% less than A" describe the same gap, because the base changes.
- check_circleAdding successive changes. A 10% rise and a 5% fall give 4.5%, not 5%. Multiply, do not add.
- check_circleMixing percent and percentage points. A rate going from 8% to 10% is a rise of 2 percentage points, but 25% in percent terms.
- check_circleThinking a rise and an equal fall cancel out. A 20% rise then a 20% fall leaves you at 96% of the start.
- check_circleReading a pass or fail question the wrong way round. "Fails by 28" means the pass mark is 28 more than the score.
How Bank and SSC Papers Test This
In IBPS PO, percentage is listed under arithmetic in the Quantitative Aptitude syllabus. The prelims section has 35 questions for 30 marks, and mains has Data Analysis & Interpretation with 40 questions for 60 marks. In data interpretation sets, many questions ask for a percentage change or a percentage share of a total.
In SSC CGL, "Percentage, Profit & Loss" is a listed topic in the Tier 1 Quantitative Aptitude section (25 questions, 50 marks), and it carries into the Tier 2 Mathematical Abilities section.
FAQs
What is the formula for percentage change?expand_more
Percentage change = (new value − old value) ÷ old value × 100. The base is always the old value.
How do you solve successive percentage change questions?expand_more
Turn each change into a multiplier (a 10% rise is 1.10, a 5% fall is 0.95) and multiply them. 1.10 × 0.95 = 1.045, a net rise of 4.5%.
Which percentage to fraction values should I learn?expand_more
At least 1/2 to 1/10, plus 1/12 (8⅓%), 1/16 (6.25%) and the multiples of 1/8 (12.5%, 37.5%, 62.5%, 87.5%).
If A is x% more than B, by how much is B less than A?expand_more
By x ÷ (100 + x) × 100 percent. For x = 25, that is 25 ÷ 125 × 100 = 20%.
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