Exam-based percentage questions are often simple in concept but tricky in wording. The main challenge is to identify the question type quickly: direct percentage, reverse percentage, increase or decrease, comparison, successive change, or a mixed arithmetic problem.
This page focuses on practice patterns that are common in competitive-exam arithmetic. The examples here are for learning and practice. They should not be treated as official previous-year questions unless a verified source is provided separately.
First Identify the Question Type
Before calculating, ask what kind of percentage problem you are looking at. This saves time because each type has a familiar setup.
- Direct percentage: find x% of a number.
- Part-to-whole: find what percent one number is of another.
- Increase or decrease: compare change with the original value.
- Reverse percentage: find the original value from a final value.
- Comparison: more than, less than, or relative difference.
- Successive change: more than one percentage change.
- Mixed arithmetic: percentage combined with ratio, profit-loss, marks, or data.
Pattern 1: Direct Percentage Questions
These are usually the quickest questions if your basic calculations are strong.
Example:
What is 32% of 625?
32/100 × 625 = 200.
You can also simplify before multiplying:
625/100 = 25/4, so 32 × 25/4 = 8 × 25 = 200.
Pattern 2: What Percent Is One Number of Another?
Use:
Percentage = Part / Whole × 100
Example:
What percent of 450 is 72?
72/450 × 100 = 16%.
The main trap is reversing the fraction.
Pattern 3: Percentage Increase
Example:
A value rises from 800 to 920. Find the percentage increase.
Increase = 120.
120/800 × 100 = 15%.
The original value, 800, is the base.
Pattern 4: Percentage Decrease
Example:
A price falls from 1,200 to 1,020. Find the percentage decrease.
Decrease = 180.
180/1,200 × 100 = 15%.
Pattern 5: Reverse Percentage
Reverse questions give the final value and ask for the original.
Example:
A number is increased by 15% and becomes 230. Find the original number.
After a 15% increase, the final value is 115% of the original.
Original = 230 × 100/115 = 200.
Pattern 6: More Than and Less Than
These questions test whether you understand the base value.
Example:
A is 25% more than B. If B = 240, find A.
25% of 240 = 60.
A = 240 + 60 = 300.
If the question now asks how much percent B is less than A:
Difference = 60.
60/300 × 100 = 20%.
So the reverse comparison is not 25%.
Pattern 7: Successive Percentage Change
Example:
A value increases by 20% and then decreases by 10%.
Assume the original value is 100.
- After 20% increase → 120
- After 10% decrease → 108
Final value = 108.
Net result = 8% increase.
Do not simply subtract 10 from 20 because the second change uses a different base.
Pattern 8: Marks and Score Questions
Example:
A student scores 378 marks out of 450. Find the percentage.
378/450 × 100 = 84%.
If the question instead gives 84% and total marks 450:
Marks = 84/100 × 450 = 378.
Pattern 9: Population or Quantity Change
Example:
A town has a population of 50,000. It increases by 8%. Find the new population.
Increase = 8% of 50,000 = 4,000.
New population = 54,000.
You can also use the multiplier:
50,000 × 1.08 = 54,000.
Pattern 10: Remaining Percentage
Example:
A shop sells 72% of its stock. If it had 1,250 items, how many remain?
Remaining percentage = 100% - 72% = 28%.
28% of 1,250 = 350.
Pattern 11: Mixed Percentage and Ratio
Some questions mix percentage with another arithmetic idea.
Example:
The ratio of boys to girls in a class is 3:2. What percentage of the class are girls?
Total parts = 3 + 2 = 5.
Girls = 2/5 of the class.
2/5 × 100 = 40%.
Pattern 12: Percentage in Profit and Loss
Percentage is often hidden inside profit, loss, discount, and marked-price questions.
Example:
An item is bought for ₹800 and sold for ₹920.
Profit = ₹120.
Profit percentage = 120/800 × 100 = 15%.
The base here is cost price.
Use Options to Check Your Work
In objective questions, options can help you detect a calculation error. Use them as a check, not as a replacement for understanding.
For example, if a direct percentage question should clearly produce a value smaller than the original number, an option larger than the original may be easy to reject.
Similarly, if a 10% increase on 500 is involved, the final answer should be close to 550. A result such as 5,500 clearly signals a decimal or percentage conversion mistake.
When Option Elimination Helps
Option elimination is useful when:
- the answer range is obvious;
- one or more options have the wrong sign;
- the percentage change is small but some options are extremely large;
- a fraction relationship makes some values impossible;
- you only need an approximate check after a correct setup.
Do not use elimination blindly when two options are close. In that situation, calculate accurately.
Common Exam Traps
These mistakes appear again and again in percentage practice:
- Using the final value as the base.
- Reversing part and whole.
- Assuming equal increase and decrease cancel.
- Reversing “more than” and “less than” without changing the base.
- Calculating before reading what the question actually asks.
- Using a mental shortcut when written work would be safer.
- Rounding too early.
For a deeper review, use Common Percentage Mistakes in Exams.
Worked Exam-Style Examples
These are ExamPrepWay-created practice examples for learning the method. They are not presented as verified official PYQs.
Example 1
A number is 40% greater than 150. Find the number.
40% of 150 = 60.
Required number = 150 + 60 = 210.
Example 2
A value decreases by 25% and becomes 300. Find the original value.
300 represents 75% of the original.
Original = 300 × 100/75 = 400.
Example 3
A quantity increases by 10% and then by 20%. Find the net percentage increase.
Assume 100.
100 → 110 → 132.
Net increase = 32%.
Example 4
36 students are 24% of a school group. Find the total number of students.
Total = 36 × 100/24 = 150.
Quick Practice Set
- Find 28% of 750.
- What percent of 640 is 96?
- A value rises from 500 to 575. Find the percentage increase.
- A number becomes 360 after a 20% increase. Find the original number.
- A is 30% more than B. If B = 400, find A.
- A value decreases by 20% and then increases by 25%. Find the net effect.
- A student scores 420 out of 500. Find the percentage.
- 65% of a stock is sold. If total stock is 800, how many remain?
A Simple Solving Routine for Exams
Use this short routine under time pressure:
- Read the question fully.
- Identify the base value.
- Decide the question type.
- Choose a reliable method.
- Calculate.
- Use the options to check whether the result is sensible.
This routine is usually faster than jumping into arithmetic and then correcting a setup mistake.
Continue Your Percentage Practice
Return to the Percentage Master Guide for the full learning path.
If formulas are still slowing you down, review Percentage Formulas You Must Remember. For language-heavy questions, use Percentage Word Problems Explained.
Then move to Percentage Practice Set 1 for solved practice.