Percentage Questions for SSC CGL: Quick Answer
Percentage questions in SSC CGL come in about eight patterns: basic "x% of y", "what per cent", successive change (a + b + ab/100), price-consumption, "A is more than B, B is less than A", exam pass marks, elections and mixtures/savings. Convert every percentage to a fraction (25% = 1/4, 12.5% = 1/8, 16⅔% = 1/6) and most questions take 30-45 seconds. Below are 15 fully worked examples and a practice set with answers.
Key takeaway: Successive change of a% and b% = a + b + (a × b)/100. For a rise of r%, the cut needed to return to the start is r/(100 + r) × 100%. These two formulas solve most SSC CGL percentage questions.
Every answer here was checked with exact fraction arithmetic in Python before publishing. For mental-maths tricks, see our percentage tricks for SSC CGL note; this page is the question bank.
Percentage Formulas and Fraction Table for SSC CGL
| Pattern | Formula |
|---|---|
| x% of y | x × y / 100 |
| A is what % of B | A / B × 100 |
| Percentage change | (New − Old) / Old × 100 |
| Successive change a%, b% | a + b + ab/100 (use − for a decrease) |
| A is r% more than B → B is less than A by | r / (100 + r) × 100% |
| A is r% less than B → B is more than A by | r / (100 − r) × 100% |
| Price up r%, cut consumption to keep spending same | r / (100 + r) × 100% |
| Price down r%, raise consumption to keep spending same | r / (100 − r) × 100% |
| Population growth at r% for n years | P(1 + r/100)ⁿ |
| Percentage | Fraction | Percentage | Fraction |
|---|---|---|---|
| 50% | 1/2 | 12.5% | 1/8 |
| 33⅓% | 1/3 | 11.11% | 1/9 |
| 25% | 1/4 | 10% | 1/10 |
| 20% | 1/5 | 9.09% | 1/11 |
| 16⅔% | 1/6 | 8⅓% | 1/12 |
| 14.28% | 1/7 | 6.25% | 1/16 |
Basic Percentage Questions for SSC CGL
Example 1: Find x% of a number
Q. Find 35% of 840.
Solution: 35% = 7/20. 840 × 7/20 = 294.
Example 2: What per cent is one number of another
Q. 45 is what per cent of 360?
Solution: 45/360 × 100 = 1/8 × 100 = 12.5%.
Example 3: Chain of percentages
Q. Find 20% of 30% of 40% of 5,000.
Solution: 5,000 × 0.4 = 2,000; × 0.3 = 600; × 0.2 = 120.
Example 4: Find the number from a percentage increase
Q. When a number is increased by 15%, it becomes 230. Find the number.
Solution: 115% of N = 230 → N = 230 × 100/115 = 200.
Successive Percentage Change Questions for SSC CGL
Example 5: Increase then decrease by the same per cent
Q. The price of an article is increased by 20% and then decreased by 20%. What is the net change?
Solution: 20 − 20 + (20 × −20)/100 = −4%, that is, a net decrease of 4%.
Why it is not zero: the 20% decrease is applied to a larger base (120), so it removes more than was added.
Example 6: Two successive increases
Q. A number is increased by 10% and then by 20%. Find the total percentage increase.
Solution: 10 + 20 + (10 × 20)/100 = 32%.
Example 7: Area change when length and breadth change
Q. The length of a rectangle is increased by 20% and its breadth decreased by 10%. Find the percentage change in area.
Solution: 20 − 10 + (20 × −10)/100 = 10 − 2 = 8% increase.
Example 8: Population growth
Q. The population of a town is 50,000. It increases by 10% every year. What will it be after 2 years?
Solution: 50,000 × 1.1 × 1.1 = 60,500.
Price and Consumption Percentage Questions
Example 9: Price rises, consumption must fall
Q. The price of sugar rises by 25%. By what per cent must a family cut its consumption so that its expenditure does not change?
Solution: r/(100 + r) × 100 = 25/125 × 100 = 20%.
Check: price 1 → 1.25, consumption 1 → 0.8; spending 1.25 × 0.8 = 1. ✓
Example 10: Income and expenditure change, savings change
Q. A man spends 75% of his income. His income rises by 20% and his expenditure by 10%. By what per cent do his savings increase?
Solution: Take income = 100. Expenditure = 75, savings = 25. New income = 120, new expenditure = 75 × 1.1 = 82.5, new savings = 37.5. Increase = 12.5/25 × 100 = 50%.
"More Than / Less Than" Percentage Questions
Example 11: A is more than B, so B is less than A by?
Q. A's salary is 25% more than B's. By what per cent is B's salary less than A's?
Solution: 25/(100 + 25) × 100 = 20%.
Example 12: Two numbers compared through a third
Q. Two numbers are 30% and 40% less than a third number. The first number is what per cent of the second?
Solution: First = 70, second = 60 (taking the third as 100). 70/60 × 100 = 116⅔%.
Percentage Questions on Exams, Elections and Mixtures
Example 13: Pass marks
Q. A student needs 40% to pass. He gets 180 marks and fails by 20 marks. Find the maximum marks.
Solution: Pass mark = 180 + 20 = 200 = 40% of maximum. Maximum = 200 × 100/40 = 500.
Example 14: Election with two candidates
Q. In an election between two candidates, the winner gets 58% of the votes and wins by 1,440 votes. All votes were valid. Find the total votes polled.
Solution: Margin = 58% − 42% = 16% of total = 1,440. Total = 1,440 × 100/16 = 9,000.
Example 15: Adding water to change the percentage
Q. A 40-litre mixture of milk and water has 10% water. How much water must be added so that water becomes 20% of the new mixture?
Solution: Milk = 36 L, which stays fixed. In the new mixture milk is 80%, so total = 36 / 0.8 = 45 L. Water to add = 45 − 40 = 5 litres.
How to Solve Percentage Questions Fast in SSC CGL
- Convert to fractions first. 37.5% = 3/8 is faster than multiplying by 0.375.
- Take 100 as the base in "income, price, population" questions.
- Use a + b + ab/100 for any two successive changes, including length × breadth.
- Watch the base. "A more than B" uses B as the base; "B less than A" uses A.
- In mixtures, fix the quantity that does not change (milk when water is added).
- Check with the options. If the answer must be a whole number of votes or marks, eliminate fractions.
Common Mistakes in Percentage Questions
| Mistake | Correct approach |
|---|---|
| +20% then −20% = 0% | Net change is −4% |
| "A is 25% more than B" so "B is 25% less than A" | B is 20% less than A |
| Adding successive increases (10% + 20% = 30%) | 10 + 20 + 2 = 32% |
| In elections, using the winner's share as the margin | Margin = winner% − loser% |
| Changing the milk amount when only water is added | Milk stays constant |
Percentage Questions for SSC CGL: Practice Set with Answers
- Find 25% of 30% of 800.
- If A is 20% more than B, by what per cent is B less than A?
- The price of rice falls by 20%. By what per cent can a family increase consumption without changing expenditure?
- Find a single discount equal to successive discounts of 20% and 10%.
- A town's population of 8,000 grows by 5% a year. Find it after 2 years.
- x is 60% of y. y is what per cent of x?
- A number decreased by 12% becomes 528. Find the number.
- Each side of a square is increased by 10%. Find the percentage increase in area.
Answers and explanations
- 60. 800 × 0.3 = 240; 240 × 0.25 = 60.
- 16⅔%. 20/120 × 100.
- 25%. 20/80 × 100.
- 28%. 20 + 10 − (20 × 10)/100 = 28.
- 8,820. 8,000 × (21/20)².
- 166⅔%. y/x = 100/60.
- 600. 528 × 100/88.
- 21%. 10 + 10 + (10 × 10)/100.
Percentage Questions for SSC CGL: FAQs
How many percentage questions come in SSC CGL Tier 1?
SSC does not publish topic-wise counts. Percentage appears in most shifts directly and is also used inside profit and loss, interest, DI and mixture questions, so it is one of the most important arithmetic topics.
What is the successive percentage formula?
For two changes of a% and b%, the net change is a + b + ab/100. Use a negative sign for a decrease.
What is the fastest way to calculate percentages in SSC CGL?
Learn the fraction table (1/2 to 1/16). Then 37.5% of 640 becomes 3/8 × 640 = 240 in one step.
Is percentage important for SSC CGL Tier 2?
Yes. Tier 2 Mathematics has more arithmetic questions, and percentage logic is used in profit and loss, interest, ratio and data interpretation.
How do I solve price and consumption questions?
If the price rises by r%, consumption must fall by r/(100 + r) × 100% to keep spending the same; if the price falls by r%, consumption can rise by r/(100 − r) × 100%.
Practice Next: SSC CGL Percentage Mock Tests
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- SSC CGL Percentage Mock Test 01
- SSC CGL Percentage Mock Test 02
- SSC CGL Percentage Mock Test 03
- SSC CGL Percentage and Profit and Loss Practice Set 01
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