PPT: Percentages | Quantitative Aptitude (Quant) - CAT PDF Download

 Page 1


Percentages
Page 2


Percentages
Introduction to Percentages
What is a Percentage?
"Percent" means "per hundred. " It's a way to express a number as a fraction of 100. 
E xa mp le: 20% = 20/100 = 0.2.
Calculation Formula
Percentage = (Part/Whole) × 100. 
E xa mp le: Ana scores 20 out of 40. 
Percentage = 
(20/40) × 100 = 50%.
Why It Matters
Percentages are crucial in competitive exams as they form the basis for solving problems in 
profit-loss, data interpretation, and comparisons. Mastery of percentages enables quicker 
calculations and better accuracy under time constraints.
Page 3


Percentages
Introduction to Percentages
What is a Percentage?
"Percent" means "per hundred. " It's a way to express a number as a fraction of 100. 
E xa mp le: 20% = 20/100 = 0.2.
Calculation Formula
Percentage = (Part/Whole) × 100. 
E xa mp le: Ana scores 20 out of 40. 
Percentage = 
(20/40) × 100 = 50%.
Why It Matters
Percentages are crucial in competitive exams as they form the basis for solving problems in 
profit-loss, data interpretation, and comparisons. Mastery of percentages enables quicker 
calculations and better accuracy under time constraints.
Basic Concepts
Base Value
The "whole" or 
denominator in any 
percentage calculation. 
Example: In "25% of 200, " 
200 is the base.
Percent Change
Measures change over 
time. 
Formula: 
Percentage 
Increase/Decrease
1. Increase by a%: 
New Value = 
Original × (1 + a/100). 
2. Decrease by a%:
 New Value = 
Original × (1 - a/100)
Page 4


Percentages
Introduction to Percentages
What is a Percentage?
"Percent" means "per hundred. " It's a way to express a number as a fraction of 100. 
E xa mp le: 20% = 20/100 = 0.2.
Calculation Formula
Percentage = (Part/Whole) × 100. 
E xa mp le: Ana scores 20 out of 40. 
Percentage = 
(20/40) × 100 = 50%.
Why It Matters
Percentages are crucial in competitive exams as they form the basis for solving problems in 
profit-loss, data interpretation, and comparisons. Mastery of percentages enables quicker 
calculations and better accuracy under time constraints.
Basic Concepts
Base Value
The "whole" or 
denominator in any 
percentage calculation. 
Example: In "25% of 200, " 
200 is the base.
Percent Change
Measures change over 
time. 
Formula: 
Percentage 
Increase/Decrease
1. Increase by a%: 
New Value = 
Original × (1 + a/100). 
2. Decrease by a%:
 New Value = 
Original × (1 - a/100)
PYQ
A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At 
the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of 
the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of 
the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is    
Ans: 340
Sol: Assume the total number of fruits = 5n.
So, the number of mangoes = (40/100)*5n = 2n.
Assume the number of apples = 5m.
He sold n mangoes, 96 bananas and 2m apples which is equal to 50% of the total fruits.
n + 96 + 2m = 2.5n
2n + 192 + 4m = 5n
192 + 4m = 3n
The smallest value of m which will satisfy the equation is m = 3.
192 + 12 = 204 = 3n
n = 68
The smallest possible total number of fruits in the stock at the beginning of the day is 5n = 5*68 = 
340.
Hence, 340 is the required answer
Page 5


Percentages
Introduction to Percentages
What is a Percentage?
"Percent" means "per hundred. " It's a way to express a number as a fraction of 100. 
E xa mp le: 20% = 20/100 = 0.2.
Calculation Formula
Percentage = (Part/Whole) × 100. 
E xa mp le: Ana scores 20 out of 40. 
Percentage = 
(20/40) × 100 = 50%.
Why It Matters
Percentages are crucial in competitive exams as they form the basis for solving problems in 
profit-loss, data interpretation, and comparisons. Mastery of percentages enables quicker 
calculations and better accuracy under time constraints.
Basic Concepts
Base Value
The "whole" or 
denominator in any 
percentage calculation. 
Example: In "25% of 200, " 
200 is the base.
Percent Change
Measures change over 
time. 
Formula: 
Percentage 
Increase/Decrease
1. Increase by a%: 
New Value = 
Original × (1 + a/100). 
2. Decrease by a%:
 New Value = 
Original × (1 - a/100)
PYQ
A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At 
the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of 
the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of 
the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is    
Ans: 340
Sol: Assume the total number of fruits = 5n.
So, the number of mangoes = (40/100)*5n = 2n.
Assume the number of apples = 5m.
He sold n mangoes, 96 bananas and 2m apples which is equal to 50% of the total fruits.
n + 96 + 2m = 2.5n
2n + 192 + 4m = 5n
192 + 4m = 3n
The smallest value of m which will satisfy the equation is m = 3.
192 + 12 = 204 = 3n
n = 68
The smallest possible total number of fruits in the stock at the beginning of the day is 5n = 5*68 = 
340.
Hence, 340 is the required answer
Absolute Value Change vs. Percentage 
Change
Absolute Change
Actual difference: Final Value - Initial Value. 
Example: Price from ?100 to ?120. 
Absolute change = ?20.
Percentage Change
Relative to original value. 
Example: ((120 - 100)/100) × 100 = 20%.
Key Insight: Same absolute change, different percentage change based on base value.