Percentage word problems become much easier when you stop trying to calculate immediately. First translate the sentence into a simple mathematical relationship. Identify the whole, the part, the percentage, and the value that the question actually wants.
Words such as of, out of, more than, less than, increased by, and remaining tell you how the numbers are related. Learning to notice these words is often more useful than memorising another shortcut.
Use a Four-Step Method
For most percentage word problems, follow this order:
- Identify what is given.
- Decide which value is the base or whole.
- Translate the words into a percentage relationship.
- Calculate only after the relationship is clear.
A useful mental pattern is:
Words → relationship → formula → calculation
Understand What “Percent of” Means
When a question says x% of a number, the word “of” usually means multiplication.
For example, 35% of 400 means:
35/100 × 400 = 140.
So if 35% of 400 students play cricket, 140 students play cricket.
Find the Part When the Whole Is Given
These questions give the total and ask you to find a percentage of it.
Use:
Part = Percentage/100 × Whole
Example: 40% of a class are girls and the class has 120 students.
Girls = 40/100 × 120 = 48.
Here, 120 is the whole and 48 is the required part.
Find the Whole When the Part Is Given
Reverse percentage questions often give a part and tell you what percentage of the total it represents.
Example: 48 students are 60% of a class. Find the total number of students.
Let total students = x.
60% of x = 48.
60/100 × x = 48.
x = 48 × 100/60 = 80.
The key is recognising that 48 is not the whole. It is only 60% of the whole.
Translate “Out of” Questions
The phrase “out of” usually identifies a part and a total.
Example: A student answers 72 questions correctly out of 90. What percentage of the questions were correct?
Percentage = 72/90 × 100 = 80%.
The number after “out of” is normally the whole in this type of question.
Handle “More Than” Carefully
If A is 20% more than B, B is the base value.
Suppose B = 500.
20% of 500 = 100.
Therefore:
A = 500 + 100 = 600.
You can also write:
A = 120% of B
or:
A = 1.20 × B.
Handle “Less Than” Carefully
If A is 20% less than B, again B is the base.
Suppose B = 500.
20% of 500 = 100.
A = 500 - 100 = 400.
So:
A = 80% of B.
Do Not Reverse Comparisons Directly
A common word-problem trap is assuming that “20% more” reverses to “20% less.”
If A is 20% more than B, take B = 100. Then A = 120.
Now B is less than A by 20, but the base is 120:
20/120 × 100 = 16.67% approximately.
So B is about 16.67% less than A, not 20% less.
Recognise “Remaining” Percentage
Some questions give the percentage used, spent, passed, sold, or completed and ask for what remains.
If 65% of a quantity is used:
Remaining percentage = 100% - 65% = 35%.
Example: A shop sells 65% of 800 items.
Items remaining = 35% of 800 = 280.
Finding the complement first often makes these questions simpler.
Percentage Increase in Word Problems
When a quantity rises from an old value to a new value, first find the increase and then compare it with the original value.
Example: A town's population increases from 20,000 to 23,000.
Increase = 3,000.
Percentage increase = 3,000/20,000 × 100 = 15%.
The original population, 20,000, is the base.
Percentage Decrease in Word Problems
Use the same logic when a value falls.
Example: The price of an item falls from ₹800 to ₹680.
Decrease = ₹120.
Percentage decrease = 120/800 × 100 = 15%.
Do not divide by ₹680 because that is the final value.
Find the Original Value After an Increase
A reverse word problem may give the final value after a percentage increase.
Example: After a 25% increase, a salary becomes ₹25,000. Find the original salary.
After a 25% increase, the final salary is 125% of the original.
Original salary = 25,000 × 100/125 = ₹20,000.
Do not simply subtract 25% of ₹25,000. The 25% increase was based on the original salary, not the final salary.
Find the Original Value After a Decrease
Example: After a 20% discount, an item costs ₹960. Find its original price.
After a 20% decrease, ₹960 represents 80% of the original price.
Original price = 960 × 100/80 = ₹1,200.
Marks and Exam Percentage Problems
Marks questions usually involve obtained marks, total marks, or a required percentage.
Example: A student scores 378 marks out of 450.
Percentage = 378/450 × 100 = 84%.
If instead the question says a student scored 84% and the examination was worth 450 marks:
Marks obtained = 84/100 × 450 = 378.
Notice how the same numbers can produce different question types depending on what is missing.
Income and Expenditure Problems
Percentage questions involving income, expenditure, and savings require you to identify what each percentage is based on.
Example: A person earns ₹40,000 per month and spends 75% of the income.
Expenditure = 75% of 40,000 = ₹30,000.
Savings = ₹40,000 - ₹30,000 = ₹10,000.
You could also notice that savings are 25% of income.
Successive Change Word Problems
When a value changes more than once, each percentage normally acts on the updated value.
Example: A price increases by 20% and then decreases by 10%.
Assume the original price is 100.
- After 20% increase → 120
- After 10% decrease → 108
The final value is 108, so the net result is an 8% increase.
Do not calculate 20% - 10% = 10% because the second change has a different base.
Worked Word Problems
These examples show how to translate the wording before calculating.
Example 1: Students in a School
In a school, 35% of 400 students play cricket. How many students play cricket?
Required part = 35% of 400.
35/100 × 400 = 140 students.
Example 2: Find the Total
54 students represent 45% of a group. Find the total number of students.
45% of total = 54.
Total = 54 × 100/45 = 120.
Example 3: More Than
Ravi's score is 25% more than Amit's score. Amit scored 240 marks. Find Ravi's score.
25% of 240 = 60.
Ravi's score = 240 + 60 = 300.
Example 4: Remaining Quantity
A tank is 72% full. If its capacity is 500 litres, how much space is empty?
Empty percentage = 100% - 72% = 28%.
28% of 500 = 140 litres.
Common Reading Mistakes
Before solving, watch for these common errors:
- Using the final value as the base instead of the original value.
- Confusing “20% of” with “20% more than.”
- Reversing a percentage comparison without changing the base.
- Calculating before identifying what the question asks.
- Ignoring words such as remaining, decreased, original, or total.
- Adding successive percentage changes directly.
For more examples of these traps, read Common Percentage Mistakes in Exams.
Quick Practice
- In a school, 35% of 400 students play cricket. How many play cricket?
- If 48 students are 60% of a class, find the total class strength.
- A price rises from ₹600 to ₹750. Find the percentage increase.
- After a 20% discount, an item costs ₹1,600. Find its original price.
- A is 25% more than B. If B = 320, find A.
- 70% of a stock is sold. If the original stock was 900 units, how many remain?
- A value increases by 10% and then decreases by 10%. Find the net effect.
A Simple Exam Checklist
Before writing your final answer, check four things:
- What is the whole or original value?
- What percentage relationship does the sentence describe?
- Am I finding a percentage, a part, the whole, or a changed value?
- Does the answer make sense compared with the numbers in the question?
This short check can prevent many errors without adding much solving time.
Continue Your Percentage Study
Return to the Percentage Master Guide for the complete percentage learning path.
If you need the equations behind these problems, review Percentage Formulas You Must Remember. For faster calculations, use Percentage Shortcuts for Arithmetic Speed.
Then apply the ideas in Percentage Practice Set 1.