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.
What You'll Learn
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
How to Solve Percentage Problems Problems
Step 1: Identify what is being asked (profit %, cost price, selling price, etc.)
Step 2: Translate each statement into mathematical relationships
Step 3: Check if Statement (1) alone yields a unique answer
Step 4: Check if Statement (2) alone yields a unique answer
Step 5: Combine statements if neither alone is sufficient
Step 6: Verify that the combination gives a unique answer
Step 7: Select the appropriate DS answer choice
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
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Percentage Problems. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Percentage Problems is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Percentage Problems?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: