Percentage Problems

Percentage Problems Data Sufficiency involve determining sufficiency for questions about percentages, profit/loss, discounts, and percentage changes. You must assess if statements provide enough information to calculate the required percentage or value.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 hoursHours to Master

Introduction to Percentage Problems

Percentage Problems Data Sufficiency involve determining sufficiency for questions about percentages, profit/loss, discounts, and percentage changes. You must assess if statements provide enough information to calculate the required percentage or value.

Prerequisites

Percentage calculations Profit, loss, discount formulas Percentage increase/decrease Standard DS answer choices
Why This Matters: Percentage Problems appear in 1-2 questions in CAT, GMAT, and Banking PO exams. They test percentage concepts and sufficiency reasoning.

How to Solve Percentage Problems Problems

1

Step 1: Identify what is being asked (profit %, cost price, selling price, etc.)

2

Step 2: Translate each statement into mathematical relationships

3

Step 3: Check if Statement (1) alone yields a unique answer

4

Step 4: Check if Statement (2) alone yields a unique answer

5

Step 5: Combine statements if neither alone is sufficient

6

Step 6: Verify that the combination gives a unique answer

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Step 7: Select the appropriate DS answer choice

Pro Strategy: For profit/loss problems, CP = SP/(1 + P%) when profit, CP = SP/(1 - L%) when loss. Check if each statement gives a unique CP value.

Example Problem

Example: What is the cost price of the article? Statement (1): Selling price is Rs. 1200 and profit is 20%. Statement (2): If sold at Rs. 900, the loss would be 10%. Solution: Step 1: Question asks for cost price Step 2: Statement (1): CP = 1200/1.2 = Rs. 1000 → SUFFICIENT alone Step 3: Statement (2): CP = 900/0.9 = Rs. 1000 → SUFFICIENT alone Answer: Each statement alone is sufficient

Pro Tips & Tricks

  • Profit % = (SP - CP)/CP × 100%, Loss % = (CP - SP)/CP × 100%
  • SP = CP × (1 + P%/100) for profit, SP = CP × (1 - L%/100) for loss
  • A single statement giving both SP and profit% is sufficient to find CP
  • A single statement giving both SP and loss% is sufficient to find CP
  • Statements with only percentage without absolute value are usually insufficient
  • Two statements with different scenarios can be sufficient together

Shortcut Methods to Solve Faster

SP + Profit% → CP = SP × 100/(100 + P%)
SP + Loss% → CP = SP × 100/(100 - L%)
Only percentages (no absolute values) → insufficient alone
Two different SP/percentage pairs → may be sufficient together

Common Mistakes to Avoid

Confusing profit percentage with markup percentage
Using wrong base (CP vs SP) for percentage calculation
Assuming percentage without absolute value is sufficient
Forgetting that profit/loss is calculated on cost price

Exam Importance

Percentage Problems is an important topic for various competitive exams. Here's how frequently it appears:

CAT
1-2 questions
GMAT
1-2 questions
BANKING PO
2-3 questions
SSC CGL
1-2 questions
INSURANCE
1-2 questions

Ready to Master Percentage Problems?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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