Percentage Notes for SSC and Railway Exams
Formulas, shortcuts and solved questions that help you understand the calculation before you try to increase your speed.
Percentage looks easy when the question simply asks for 20% of a number. The confusion usually starts when a price changes twice, a salary increases, or the question asks how much one value is less than another. Many students know the formula but still choose the wrong number as the base.
These Percentage Notes for SSC and Railway Exams explain the chapter from that basic point. You will learn how to choose the base, convert percentages into fractions, use short methods and solve common arithmetic questions without making the calculation unnecessarily long.
Percentage is listed in the official SSC CGL syllabus and the RRB NTPC Graduate notification. The same basic methods also help you study profit and loss, interest, discounts and data interpretation. Match your final preparation with the notification for your own exam.
What is percentage? Percentage means a value expressed out of 100. To find what percentage a part is of a whole, use (Part ÷ Whole) × 100. In increase or decrease questions, divide the change by the original value.
What Does Percentage Mean?
The word percent means per hundred. So 25% means 25 out of 100. You can write it as 25/100, 1/4 or 0.25. These are different ways of showing the same value.
Imagine a class of 100 students. If 25 students travel by bus, then 25% of the class travels by bus. If the class has 200 students, 25% means 50 students. The percentage stays the same, but the actual number changes with the total.
The base value is the number treated as 100%. In the class example, the total number of students is the base.
The complete grid represents the base, or 100%.
How to Choose the Correct Base
Before calculating, ask: “Percentage of which value?” In “30 is what percent of 150?”, the base is 150. In “a price rises from 150 to 180”, the base is the old price, 150.
If fractions and ratios still feel confusing, practise the ratio and proportion questions with solutions after this section. Percentage is easier when you can recognise the relationship between a part and the whole.
Percentage to Fraction Conversion Chart
You do not need to multiply by 100 in every calculation. Familiar fractions make many percentage questions shorter. For example, 12.5% of 640 is simply 640 ÷ 8.
| Percentage | Exact fraction | Quick operation on N |
|---|---|---|
| 1% | 1/100 | N ÷ 100 |
| 5% | 1/20 | N ÷ 20 |
| 10% | 1/10 | N ÷ 10 |
| 12.5% | 1/8 | N ÷ 8 |
| 16 2/3% | 1/6 | N ÷ 6 |
| 20% | 1/5 | N ÷ 5 |
| 25% | 1/4 | N ÷ 4 |
| 33 1/3% | 1/3 | N ÷ 3 |
| 37.5% | 3/8 | (N ÷ 8) × 3 |
| 40% | 2/5 | (N ÷ 5) × 2 |
| 50% | 1/2 | N ÷ 2 |
| 62.5% | 5/8 | (N ÷ 8) × 5 |
| 66 2/3% | 2/3 | (N ÷ 3) × 2 |
| 75% | 3/4 | (N ÷ 4) × 3 |
| 80% | 4/5 | (N ÷ 5) × 4 |
| 87.5% | 7/8 | (N ÷ 8) × 7 |
Reading mixed fractions: 16 2/3% means sixteen and two-thirds percent. It is exactly 1/6 of the base. Using 16.67% instead introduces rounding, so keep the fraction when the question allows it.
Decimal conversion: Divide a percentage by 100 to write it as a decimal: 35% = 0.35. Multiply a decimal by 100 to write it as a percentage: 0.08 = 8%.
Important Percentage Formulas for SSC and Railway Exams
In this percentage formula sheet, N is the whole or original number, A is the part, and p is the percentage number. For example, use p = 20 when the question says 20%.
| Question type | Formula |
|---|---|
| Find p% of N | (p ÷ 100) × N |
| A is what percent of N? | (A ÷ N) × 100; N must not be zero |
| p% of N equals A; find N | (A × 100) ÷ p; p must not be zero |
| Percentage increase | [(New − Old) ÷ Old] × 100 |
| Percentage decrease | [(Old − New) ÷ Old] × 100 |
| Value after a p% increase | Old × (100 + p) ÷ 100 |
| Value after a p% decrease | Old × (100 − p) ÷ 100 |
| Two successive changes, a% and b% | Net change = a + b + (ab ÷ 100), in percent. Use negative rates for decreases. |
| Increase needed after a p% fall | [p ÷ (100 − p)] × 100%; for 0 < p < 100 |
| If A is p% more than B, how much less is B than A? | [p ÷ (100 + p)] × 100% |
| If A is p% less than B, how much more is B than A? | [p ÷ (100 − p)] × 100%; for 0 < p < 100 |
The old value must be positive in the usual increase and decrease questions in these notes. If the old value is zero, the usual percentage-change formula is undefined because it would divide by zero.
Three or more changes: Multiply the factors. For +10%, −20% and +25%, use 1.10 × 0.80 × 1.25 = 1.10. The final value is 110% of the original, so the net increase is 10%.
Percentage Shortcuts with Simple Examples
1. Find 10%, 5% and 1% First
For 360, 10% is 36, 5% is half of 36, or 18, and 1% is 3.6. You can combine these pieces. So 15% of 360 = 36 + 18 = 54.
2. Replace Familiar Percentages with Fractions
To find 37.5% of 560, use 3/8. First calculate 560 ÷ 8 = 70, then 70 × 3 = 210. This is often easier than multiplying 560 by 37.5 and dividing by 100.
3. Use x% of y = y% of x
Both expressions equal xy/100, so you can swap the two numbers when it makes the calculation easier. For example, 48% of 25 = 25% of 48 = 12.
4. Assume 100 When Only Relative Values Matter
If a question gives only percentage changes and asks for the net change, start with 100. This makes each change visible. Use the actual starting value when the question asks for an amount in rupees, people or another unit.
5. Use the Multiplier for Repeated Changes
A 12% increase means multiplying by 1.12. An 8% decrease means multiplying by 0.92. For a population of 10,000 growing by 10% in each of two years, calculate 10,000 × 1.10 × 1.10 = 12,100. The total increase is 21%, because the second increase uses the new population.
The same idea helps with interest. After learning the percentage base properly, try the simple interest questions with detailed solutions to practise applying a rate to a principal.
Percentage Questions with Step-by-Step Solutions
These are original exam-style practice examples. Work through the method first, then cover the solution and solve the same question yourself.
Find a percentage of a number
Question: Find 35% of 480.
Answer: 168.
Splitting 35% into 30% and 5% keeps the calculation short.
Find what percent one number is of another
Question: 72 is what percent of 240?
Answer: 30%.
The words “of 240” tell you that 240 is the base.
Find the original number
Question: 18% of a number is 126. Find the number.
Answer: 700.
Check: 10% of 700 is 70 and 8% is 56. Together, they give 126.
Calculate a percentage increase
Question: A monthly allowance rises from Rs. 8,000 to Rs. 9,200. Find the percentage increase.
Answer: 15% increase.
Use the old allowance, Rs. 8,000, as the denominator.
Solve successive percentage changes
Question: A price increases by 20% and then decreases by 15%. Find the net change.
Answer: 2% increase.
Using signed rates gives the same answer: 20 + (−15) + [20 × (−15)/100] = 2.
Successive changes also appear in selling-price questions. Apply the same method in the profit and loss practice test after completing these examples.
Compare “more than” with “less than”
Question: A earns 25% more than B. By what percentage does B earn less than A?
Answer: 20% less.
The first comparison uses B as the base. The second comparison uses A as the base.
Recover after a percentage decrease
Question: A value falls by 25%. What percentage increase is needed to return to the original value?
Answer: 33 1/3% increase.
The recovery percentage is calculated on 75, the reduced value.
Keep expenditure unchanged when price rises
Question: The price of rice rises by 25%. By what percentage should consumption fall to keep total expenditure unchanged?
Answer: Consumption must fall by 20%.
For a p% price rise, the consumption reduction is [p/(100 + p)] × 100%, provided the same total budget buys the same item.
Find the percentage change in savings
Question: A person earns Rs. 30,000 and spends 80% of it. Income rises by 20% and expenditure rises by 10%. Find the percentage increase in savings.
Answer: Savings increase by 60%.
The 10% rise in expenditure applies to the old expenditure, not to the new income.
Find total marks and passing marks
Question: A student scoring 35% fails by 12 marks. Another student scoring 45% gets 18 marks more than the passing marks. Find the maximum marks and passing marks.
Answer: Maximum marks = 300; passing marks = 117.
Use the information given in the question. Do not assume that passing marks must be 40%.
Solve an election percentage question
Question: In an election with two candidates, the winner gets 56% of all valid votes and wins by 960 votes. Find the total valid votes.
Answer: 8,000 valid votes.
The two-candidate condition matters. Both percentages here use total valid votes as the base.
Find the combined percentage
Question: Class A has 40 students and a 60% pass rate. Class B has 60 students and an 80% pass rate. Find the combined pass percentage.
Answer: 72%.
The class sizes differ, so the simple average of 60% and 80% would give the wrong combined percentage.
For more table-based percentage comparisons, attempt the data interpretation questions with solutions. Always check whether the data asks for a share, a difference or a change.
Percentage vs Percentage Points
These two expressions describe different things. If a pass rate rises from 40% to 50%, the difference is 10 percentage points. The percentage increase in the pass rate is 25%, because 10 is 25% of the old rate, 40.
| What is asked? | Calculation | Answer |
|---|---|---|
| Difference in percentage points | 50 − 40 | 10 percentage points |
| Relative percentage increase | [(50 − 40)/40] × 100 | 25% increase |
Read the wording carefully in election results, pass rates and data interpretation. A difference between two percentage figures is not automatically the percentage change in the underlying rate.
How Percentage Connects with Other Maths Topics
Profit, loss and discount: Profit and loss percentages normally use cost price as the base. Discount percentage uses marked price. A Rs. 200 profit on a cost price of Rs. 1,000 is 20%; a Rs. 200 discount on a marked price of Rs. 1,600 is 12.5%.
Population and compound growth: Repeated changes use the latest value each time. At a constant annual growth rate r%, the value after n years is P × (1 + r/100)n. Here, P is the initial value and n is the number of yearly changes.
Area change: If a rectangle’s length increases by 10% and its breadth decreases by 10%, its area becomes 1.10 × 0.90 = 0.99 times the original area. That is a 1% decrease. Both changing dimensions affect the final area.
Percentage Practice Questions for SSC and Railway Exams
Try these 10 percentage MCQs before opening the answers. Write the base beside each calculation. The questions are original practice material; they are not presented as previous-year questions.
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What is 12.5% of 640?
Show answer and method
Answer: B. 12.5% = 1/8. So 640 ÷ 8 = 80.
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45% of a number is 180. What is the number?
Show answer and method
Answer: B. Number = (180 × 100)/45 = 400.
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54 is what percent of 120?
Show answer and method
Answer: C. (54/120) × 100 = 45%.
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A value increases from 1,500 to 1,800. What is the percentage increase?
Show answer and method
Answer: C. Increase = 300. Use the old value: (300/1,500) × 100 = 20%.
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A value rises by 25% and then falls by 20%. What is the net change?
Show answer and method
Answer: C. Start with 100. After the changes, 100 × 1.25 × 0.80 = 100. There is no net change.
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A is 40% more than B. By what percentage is B less than A?
Show answer and method
Answer: B. Take B = 100 and A = 140. Required percentage = (40/140) × 100 = 200/7% = 28 4/7%.
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After a 20% decrease, a value becomes 960. What was the original value?
Show answer and method
Answer: C. The remaining value is 80% of the original. Original = (960 × 100)/80 = 1,200.
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A price rises by 20%. By what percentage must consumption fall to keep expenditure unchanged?
Show answer and method
Answer: A. Required fall = [20/(100 + 20)] × 100 = 16 2/3%.
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A student scores 35 out of 50. What is the marks percentage?
Show answer and method
Answer: C. (35/50) × 100 = 70%.
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A person earns Rs. 20,000 and spends 75% of it. Income rises by 10% and expenditure rises by 20%. How do savings change?
Show answer and method
Answer: A. Old spending = 15,000 and old savings = 5,000. New income = 22,000; new spending = 18,000; new savings = 4,000. Savings fall by (1,000/5,000) × 100 = 20%.
After checking your answers, use the SSC CGL subject-wise and topic-wise practice hub to continue with the arithmetic chapter you need next. Choose practice based on the type of mistake you made here.
Percentage Calculator for Checking Your Work
Use this small calculator after solving a question on paper. It shows the calculation so you can compare your method with the result.
Common Percentage Mistakes to Avoid
| Mistake | Correct approach |
|---|---|
| Using the new value as the base for an increase | Divide the increase by the original value. |
| Adding successive percentages directly | Apply each change to the updated value, or multiply the factors. |
| Assuming 20% more and 20% less are opposite comparisons | Write the base for each comparison. The denominators change. |
| Taking the simple average of percentages for unequal groups | Find the actual numbers first, then calculate the combined percentage. |
| Rounding 1/3 or 1/6 too early | Keep fractions until the final step when an exact answer is possible. |
| Giving a number when the question asks for a percentage | Check the required unit: rupees, marks, people or percent. |
If you understand the method but still lose marks in calculations, follow the guide to reducing calculation mistakes in competitive exams. Record whether the error came from choosing the base, reading the question or doing the arithmetic.
A Simple Three-Session Revision Plan
- First session: Learn the meaning of percentage, the base value and the fraction chart. Solve direct “percent of” and missing-number questions.
- Second session: Practise increase, decrease, successive changes and more-than/less-than comparisons. Explain the base in your own words.
- Third session: Solve mixed questions on savings, expenditure, marks, elections and data interpretation. Reattempt every question you got wrong.
Quick revision: Percentage = (Part/Whole) × 100. Change percentage = (Change/Original) × 100. For successive changes, multiply the factors. For combined groups, calculate totals before taking the percentage.
FAQs on Percentage Notes for SSC and Railway Exams
What is the basic percentage formula?
Percentage = (Part ÷ Whole) × 100, where the whole is not zero. To find p% of a number N, calculate (p/100) × N.
How can I calculate percentages quickly without a calculator?
Learn common percentage-to-fraction conversions and build values from 10%, 5% and 1%. For example, 25% means one-fourth, so 25% of 360 is 360 ÷ 4 = 90.
How do I find the original value after a percentage increase or decrease?
After a p% increase, divide the new value by (1 + p/100). After a p% decrease, divide it by (1 − p/100), provided that factor is not zero. For example, 960 after a 20% fall means 960 ÷ 0.80 = 1,200 originally.
Why does a 20% rise followed by a 20% fall give a loss?
The second change uses a larger base. Starting from 100, a 20% rise gives 120. A 20% fall from 120 is 24, so the final value is 96, a 4% loss from the original.
Can a percentage be greater than 100?
Yes. It means the compared value is greater than the chosen base. For example, 150% of 200 is 300. In a normal marks question, however, a score cannot exceed 100% of the maximum unless the marking rules specifically allow it.
Are these percentage questions actual SSC or Railway PYQs?
These are original practice questions with worked solutions. After learning the methods, use authentic previous-year papers for your specific examination to practise the wording and difficulty of that paper.
Conclusion
Percentage becomes much easier when you stop rushing the first step. Identify the base, choose a fraction or multiplier, and check what the question actually asks. Use these percentage notes for regular revision, solve the practice questions yourself, and revisit the methods where you made mistakes.
