Ratio & Proportion – Nagaland TET (Quantitative Aptitude)
Ratio shows how two amounts compare to each other.
Proportion means “two ratios are equal”.
1. Simple Explanation
| Concept | Everyday Analogy | Quick Example |
|---|---|---|
| Ratio | Two friends share a pizza: 3 slices for Alice, 5 for Bob → 3 : 5 | 3 : 5 |
| Proportion | If Alice gets 3 slices and Bob 5, and the whole pizza has 8 slices, the same ratio holds for the whole pizza: 3/8 = 5/8? | 3 : 5 = 6 : 10 (because 6/10 = 3/5) |
2. How to Read a Ratio
- Write the numbers separated by a colon (
:). - The first number is “part one”, the second is “part two”.
Example:
4 : 7means for every 4 units of part 1, there are 7 units of part 2.
3. Reducing a Ratio
- Find the greatest common divisor (GCD) of the two numbers.
- Divide both numbers by the GCD.
Example:
12 : 18→ GCD is 6 →12 ÷ 6 : 18 ÷ 6 = 2 : 3.
4. Checking a Proportion (Cross‑Multiplication)
Two ratios a : b and c : d are in proportion when:
a × d = b × c
Tiny Example
Check if 4 : 5 and 8 : 10 are in proportion.
4 × 10 = 40
5 × 8 = 40 → equal, so yes!
5. Solving Ratios with a Missing Value
Use cross‑multiplication:
a : b = c : ?
a × ? = b × c
? = (b × c) ÷ a
Example
If 2 : 5 = 6 : ?:
2 × ? = 5 × 6
? = (5 × 6) ÷ 2 = 30 ÷ 2 = 15
So the missing number is 15.
6. Scaling a Ratio
If every part of a ratio is multiplied by the same number, the ratio stays the same.
| Original Ratio | Scale Factor | New Ratio |
|---|---|---|
3 : 4 |
2 |
6 : 8 |
5 : 7 |
3 |
15 : 21 |
Use it when you need more or fewer items but keep the same proportions.
7. Quick Tips for TET
- Read the problem carefully – find the two numbers or the “parts”.
- Simplify the ratio before using it (makes calculations easier).
- Use cross‑multiplication to check or to find a missing part.
- Check your answer by plugging it back into the ratio.
8. Mini Practice Set
| # | Problem | Quick Solution |
|---|---|---|
| 1 | A bag has 5 red and 15 blue marbles. What is the ratio red : blue? | Reduce 5 : 15 → 1 : 3. |
| 2 | 6 : 9 is in proportion to ? : 12. Find the missing number. |
6 × 12 = 9 × ? → 72 = 9 × ? → ? = 8. |
| 3 | Two friends share money 20 : 30. If the total money is 200 units, how much does each get? | Scale factor = 200 ÷ (20+30)=200 ÷ 50 = 4 → 20×4 = 80, 30×4 = 120. |
| 4 | Check if 7 : 11 and 14 : 22 are in proportion. |
7 × 22 = 154, 11 × 14 = 154 → yes. |
Answers
1 : 38- Friend A = 80 units, Friend B = 120 units
- Yes, they are in proportion.
9. Summary
- Ratio = comparison of two numbers (
a : b). - Proportion = two ratios are equal (
a : b = c : d). - Reduce ratios by dividing by the GCD.
- Cross‑multiply to check or to find missing numbers.
- Scale ratios to fit a new total.
Keep practicing with everyday items—candy, money, or recipes—and you'll master ratio & proportion in no time!