Ratio and Proportion Solved Problems (With Step-by-Step Solutions)
Ratio and proportion are important arithmetic concepts used to compare quantities and understand their relationships. These topics are widely used in real life, such as sharing money, mixing ingredients, speed calculations, and scaling values. They are also frequently asked in school exams and competitive examinations.
In this article, you will find detailed ratio and proportion solved problems with clear explanations. Each problem is explained step by step so that students can understand the method and apply it confidently.
Important Concepts
- Ratio: Comparison of two quantities of the same kind
- Proportion: Equality of two ratios
- Ratio a : b can also be written as a/b
- If a : b = c : d, then a × d = b × c
Solved Ratio & Proportion Problems
Problem 1: Simplify the ratio 18 : 24
Solution:
Step 1: Find the HCF of 18 and 24.
HCF = 6
Step 2: Divide both terms by 6.
18 ÷ 6 : 24 ÷ 6 = 3 : 4
Simplified ratio = 3 : 4
Problem 2: Divide ₹600 between A and B in the ratio 2 : 3
Solution:
Total parts = 2 + 3 = 5
A’s share = (2/5) × 600 = 240
B’s share = (3/5) × 600 = 360
A gets ₹240 and B gets ₹360
Problem 3: If 5 pens cost ₹40, what is the cost of 8 pens?
Solution:
Cost of 1 pen = 40 ÷ 5 = 8
Cost of 8 pens = 8 × 8 = 64
Cost of 8 pens = ₹64
Problem 4: The ratio of boys to girls in a class is 3 : 2. If there are 30 students in total, find the number of boys.
Solution:
Total parts = 3 + 2 = 5
Number of boys = (3/5) × 30
= 18
Number of boys = 18
Problem 5: Find the fourth proportional to 4, 6, and 10
Solution:
Let the fourth proportional be x.
4 : 6 = 10 : x
Cross-multiplying:
4 × x = 6 × 10
x = 60 ÷ 4 = 15
Fourth proportional = 15
Common Mistakes to Avoid
- Not simplifying ratios fully
- Confusing ratio with proportion
- Using incorrect total parts in sharing problems
- Ignoring units while comparing quantities
Practice Tips
✔ Always simplify ratios to lowest terms
✔ Convert word problems into ratios before solving
✔ Use proportion formula carefully
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