PPT: Ratio and Proportion | Quantitative Aptitude for SSC CGL PDF Download

 Page 1


Ratios and 
Proportions
Page 2


Ratios and 
Proportions
Introduction to Ratios, 
Proportions, and 
Variations
What are Ratios?
Comparison of two quantities (e.g., x:y or x/y).
Why Important?
Core topic in Competitive Exams.
Core Idea
Ratios express relationships; proportions and 
variations extend this concept.
Example: If A's salary is 200 and B's is 300, ratio of their 
salaries = 2:3.
Page 3


Ratios and 
Proportions
Introduction to Ratios, 
Proportions, and 
Variations
What are Ratios?
Comparison of two quantities (e.g., x:y or x/y).
Why Important?
Core topic in Competitive Exams.
Core Idea
Ratios express relationships; proportions and 
variations extend this concept.
Example: If A's salary is 200 and B's is 300, ratio of their 
salaries = 2:3.
Understanding 
Ratios
Definition
Ratio of x to y = x/y (antecedent: x, consequent: 
y).
Simplification
Remove common factors (e.g., 4:2 = 2:1).
Percentage Form
Ratio × 100 (e.g., 4/5 = 80%).
Example
Salaries 7:5 ³ 7k and 5k, k > 0.
Page 4


Ratios and 
Proportions
Introduction to Ratios, 
Proportions, and 
Variations
What are Ratios?
Comparison of two quantities (e.g., x:y or x/y).
Why Important?
Core topic in Competitive Exams.
Core Idea
Ratios express relationships; proportions and 
variations extend this concept.
Example: If A's salary is 200 and B's is 300, ratio of their 
salaries = 2:3.
Understanding 
Ratios
Definition
Ratio of x to y = x/y (antecedent: x, consequent: 
y).
Simplification
Remove common factors (e.g., 4:2 = 2:1).
Percentage Form
Ratio × 100 (e.g., 4/5 = 80%).
Example
Salaries 7:5 ³ 7k and 5k, k > 0.
PYQ
In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 6 6 6 5. They rent a 
house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective 
incomes to cover the total house rent in that month. In October, the house rent remains 
unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the 
percentage of their total income that will be paid as house rent, is nearest to 
(a)  12.75
(b)  14.84
(c)  15.18
(d)  13.26
Solution
Page 5


Ratios and 
Proportions
Introduction to Ratios, 
Proportions, and 
Variations
What are Ratios?
Comparison of two quantities (e.g., x:y or x/y).
Why Important?
Core topic in Competitive Exams.
Core Idea
Ratios express relationships; proportions and 
variations extend this concept.
Example: If A's salary is 200 and B's is 300, ratio of their 
salaries = 2:3.
Understanding 
Ratios
Definition
Ratio of x to y = x/y (antecedent: x, consequent: 
y).
Simplification
Remove common factors (e.g., 4:2 = 2:1).
Percentage Form
Ratio × 100 (e.g., 4/5 = 80%).
Example
Salaries 7:5 ³ 7k and 5k, k > 0.
PYQ
In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 6 6 6 5. They rent a 
house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective 
incomes to cover the total house rent in that month. In October, the house rent remains 
unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the 
percentage of their total income that will be paid as house rent, is nearest to 
(a)  12.75
(b)  14.84
(c)  15.18
(d)  13.26
Solution
Properties of Ratios
Scaling
If A:B = a:b, then A = ak, B = bk.
Inequality
a:b (a > b) ³ Greater inequality.
a:b (a < b) ³ Less inequality.
a:b (a = b) ³ Equality.