Ratio and Proportion
Ratio and proportion are fundamental concepts in quantitative aptitude used to compare quantities and solve real-life problems. These concepts are widely asked in competitive exams like banking, SSC, CMAT, and placements.
Fundamental Principles
Ratio
A comparison of two quantities expressed as a:b.
Proportion
An equation stating that two ratios are equal, i.e., a:b = c:d.
Continued Proportion
When a:b = b:c, then b² = ac.
Essential Formulation Tips
- Always simplify ratios to the lowest form.
- Convert units before comparing ratios.
- Use cross multiplication for solving proportions.
- Check if quantities are directly or inversely proportional.
Shortcut Execution Techniques
- If a:b = x:y, then a = kx and b = ky.
- For proportion: a:b = c:d → ad = bc.
- In mixture problems, use weighted average concept.
- If ratio changes, adjust using multiplication factors.
Contextual Inquiries (FAQs)
Q: What is the fastest way to solve ratio questions?
A:
Q: Where is ratio and proportion used in exams?
A:
Example Breakdown: Basic Ratio Example
Basic concept question.Find HCF of 12 and 18 = 6.
Divide both terms by 6.
12 : 18 = 2 : 3.
Final Answer: 2 : 3.
Example Breakdown: Proportion Example
Standard exam question.Use cross multiplication.
2 × 9 = 3 × x.
18 = 3x.
x = 6.
Final Answer: x = 6.
Example Breakdown: Word Problem Example
Most repeated exam pattern.Total ratio parts = 3 + 2 = 5.
Each part = 50 / 5 = 10.
Girls = 2 × 10 = 20.
Final Answer: 20.
Ratio & Proportion Practice Questions
Solve important ratio and proportion questions for banking, SSC, CMAT, and placement exams.
Q1. Find x if 4 : x = 2 : 5.
Q2. Divide Rs. 600 in ratio 2 : 3.
Q3. If a:b = 5:7 and b:c = 3:4, find a:c.