One-Line Definition
A Percentage is a way of expressing a number as parts out of 100. It helps compare quantities regardless of their actual size.
Pizza Slices Mental Model
Imagine a pizza cut into 100 equal slices:
- • Eat 25 slices → You've eaten 25%
- • Eat 50 slices → You've eaten 50%
- • Eat all 100 slices → You've eaten 100%
Percentages are one of the most important topics in aptitude exams because they appear directly and indirectly across almost every arithmetic topic:
Example:
Out of 40 students in a classroom, 30 students passed the examination.
Percentage Passed = (30 / 40) × 100 = 75%.
Thinking in Multipliers (Shortcut)
Memorize these core fractional equivalents to eliminate long division during CAT & MBA CET exam drills.
SHORTCUT RULES & KEY FORMULAS
AB Rule
Used when the product of two variables remains constant (Price × Consumption = Expenditure, Speed × Time = Distance).
Successive Percentage Formula
Calculates net percentage change when two successive percentage changes a% and b% are applied sequentially.
SOLVED EXAMPLES (LEVEL 0 TO HARD)
Q: Find 20% of 250.
Solution: Convert 20% into its fractional equivalent 1/5.
20% of 250 = 250 ÷ 5 = 50.
Q: A shirt costs ₹800. Its price increases by 15%. Find the new price.
Step 1: Increase amount = 15% of 800 = (15 / 100) × 800 = ₹120.
Step 2: New Price = Original Price + Increase = 800 + 120 = ₹920.
(Alternative Multiplier Method: New Price = 800 × 1.15 = ₹920)
Q: A quantity increases by 20% and then decreases by 20%. Is the final value equal to the original?
Step 1: Assume Original Value = 100.
Step 2: After 20% increase: 100 → 120.
Step 3: After 20% decrease on 120: 20% of 120 = 24. Final = 120 - 24 = 96.
Step 4: Net Change = 96 - 100 = -4% overall decrease.
Mistake 1
Adding Percentage Changes Directly
+20% followed by -20% does NOT equal 0%. It results in an overall 4% decrease. Always apply successive percentage formulas or multipliers.
Mistake 2
Using the Wrong Base Quantity
20% of 50 = 10, whereas 50% of 20 = 10 (numerical equality, but base context differs in word problems). Always identify the reference base.
Mistake 3
Incorrect Decimal Conversions
25% = 0.25 (NOT 25). 0.5% = 0.005. Be extra cautious with decimals smaller than 1%.
1. Find 30% of 150.
Answer: (30/100) × 150 = 45.
2. A salary increases from ₹40,000 to ₹46,000. Find the percentage increase.
Answer: (6,000 / 40,000) × 100 = 15% increase.
3. A product price is first increased by 25% and then discounted by 20%. Find the overall percentage change.
Answer: Net = +25 - 20 + (25 × -20)/100 = 5 - 5 = 0% overall change (Price remains same).
FREQUENTLY ASKED QUESTIONS
❓ Why are fraction to percentage tables important for CAT & CET?
Memorizing fractions from 1/2 to 1/20 turns time-consuming division into instant mental arithmetic. For example, knowing 1/7 = 14.28% and 1/8 = 12.5% saves 30-45 seconds per question.
❓ How does the AB Rule work for Price-Consumption questions?
When Expenditure = Price × Consumption is constant, a fraction increase in Price of x/y causes a fraction decrease in Consumption of x/(x+y).
❓ Can a percentage be greater than 100%?
Yes! For example, if sales double, the increase is 100%. If sales become 3 times the original amount, the increase is 200% (and total is 300% of original).