Introduction
Ratio and Proportion help compare quantities and determine relationships between values. These concepts are widely used in mathematics, aptitude tests, business calculations, and everyday problem-solving.
Question 1
The ratio of boys to girls in a class is 3:2.
If there are 30 boys, how many girls are there?
A) 15
B) 20
C) 25
D) 30
Answer
B) 20
Explanation
Ratio = 3:2
30 boys represent 3 parts.
1 part = 30 ÷ 3 = 10
Girls = 2 parts
= 2 × 10
= 20
Question 2
The ratio of two numbers is 4:5.
If the first number is 20, what is the second number?
A) 22
B) 24
C) 25
D) 30
Answer
C) 25
Explanation
4 parts = 20
1 part = 20 ÷ 4 = 5
Second number = 5 parts
= 5 × 5
= 25
Question 3
If 6 pens cost ₹90, what is the cost of 10 pens?
A) ₹120
B) ₹130
C) ₹140
D) ₹150
Answer
D) ₹150
Explanation
Cost of 1 pen
= 90 ÷ 6
= ₹15
Cost of 10 pens
= 10 × 15
= ₹150
Question 4
The ratio of red balls to blue balls is 2:3.
If there are 12 red balls, how many blue balls are there?
A) 15
B) 18
C) 20
D) 24
Answer
B) 18
Explanation
2 parts = 12
1 part = 12 ÷ 2 = 6
Blue balls = 3 parts
= 3 × 6
= 18
Question 5
If 4 workers can complete a task in 12 days, how many days will 8 workers take?
A) 4
B) 5
C) 6
D) 8
Answer
C) 6
Explanation
Workers and days are inversely proportional.
4 × 12 = 8 × x
48 = 8x
x = 6
Therefore, 8 workers will complete the task in 6 days.
Key Learning
Important Formula:
If a:b = c:d
Then
a × d = b × c
This is called the cross-multiplication rule and is useful for solving proportion questions.
Practice Tip
Always simplify ratios to their lowest form before solving problems.
Example:
10:20 = 1:2
This makes calculations much easier.
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