Ratio and Proportion
Ratio and proportion is a core aptitude topic used in percentages, profit & loss, and algebra. Strong understanding helps solve complex problems quickly in competitive exams.
Fundamental Principles
Ratio
A comparison of two quantities expressed as a:b.
Proportion
An equation that states two ratios are equal (a:b = c:d).
Inverse Proportion
When one quantity increases, the other decreases proportionally.
Essential Formulation Tips
- Simplify ratios to lowest terms.
- Convert word problems into ratios clearly.
- Use unitary method for proportion problems.
- Practice mixture and partnership questions.
Shortcut Execution Techniques
- Cross multiplication for proportion.
- If a:b = c:d → ad = bc.
- Use LCM method to combine ratios.
- Convert ratios into fractions when needed.
Contextual Inquiries (FAQs)
Q: How to solve ratio questions quickly?
A:
Q: Where are ratios used in exams?
A:
No structural solved cases documented for this level module.
Ratio & Proportion Practice Questions (Easy to Hard)
Solve ratio MCQs from basic to advanced level for competitive exams.
Q1. Simplify the ratio 10:20.
Q2. Find the ratio of 50 to 100.
Q3. If a:b = 2:3 and b:c = 4:5, find a:c.
Q4. Divide 60 in the ratio 2:3.
Q5. If 4:x = 8:16, find x.
Q6. The ratio of boys to girls is 3:2. If boys = 30, find girls.
Q7. If a:b = 5:7 and b:c = 3:4, find a:c.
Q8. Divide 1000 in the ratio 1:2:3.
Q9. If income ratio is 3:4 and expenditure ratio is 2:3, find savings ratio.
Q10. Two numbers are in ratio 5:6. Their sum is 121. Find numbers.