Quick Concept Summary
Ratio compares quantities; proportion states that two ratios are equal. These ideas appear in ages, partnership, mixtures, shares, recipes, speed, and maps.
Core Ideas
- Ratio compares like quantities
- Simplify ratios by dividing common factors
- Ratios do not show actual values unless total or difference is given
- Proportion uses cross multiplication
Worked Examples
Example 1: Divide in a ratio
Divide Rs. 720 in the ratio 3:5.
Total parts = 8
Shares = 720 × 3/8 = 270 and 720 × 5/8 = 450
Example 2: Continued ratio
If A:B = 2:3 and B:C = 4:5, find A:B:C.
Make B equal:
A:B = 8:12
B:C = 12:15
So A:B:C = 8:12:15
Example 3: Proportion
Find x if 4:7 = x:35.
4/7 = x/35
x = 20
Direct vs Inverse Proportion
| Direct Proportion | Inverse Proportion |
|---|---|
| Both quantities move same way | One rises when the other falls |
| More items, more cost | More workers, fewer days |
Practice Questions
1. Divide 960 in the ratio 5:7. 2. If A:B = 3:4 and B:C = 8:9, find A:B:C. 3. Find the fourth proportional to 6, 9, and 15. 4. If 12 workers finish a job in 15 days, how many days for 20 workers? 5. Two numbers are in ratio 7:9 and differ by 18. Find them.
Common Mistakes
- Adding ratios directly without matching the common term
- Forgetting units must match before forming a ratio
- Mixing direct and inverse proportion
Revision Checklist
- [ ] Ratio simplification
- [ ] Division in a ratio
- [ ] Continued ratio
- [ ] Direct vs inverse proportion