Ratio & Proportion – Arunachal Pradesh TET (Quantitative Aptitude)
Why it matters?
Ratio & proportion is a foundational concept in many TET quantitative questions – from price calculations to time‑distance problems, to mixture problems and more. Mastering this topic will give you confidence and speed.
1. Simple Explanation
-
Ratio – A comparison of two or more quantities by division.
A : B = 2 : 3means for every 2 units of A, there are 3 units of B. -
Proportion – An equation that states two ratios are equal.
A : B = C : DorA/B = C/D.
When you know any three parts of a proportion, you can find the fourth using the cross‑multiplication rule.
2. Key Points
| Concept | What to remember |
|---|---|
| Notation | : for ratio, = for proportion. |
| Cross‑Multiplication | If A/B = C/D ⇒ A × D = B × C. |
| Finding the Missing Term | If three terms are known, compute the fourth: |
x = (B × C)/A or x = (A × D)/C. |
|
| Direct vs Inverse Proportion |
- Direct: if one quantity increases, the other increases.
- Inverse: if one quantity increases, the other decreases. |
| Percent Increase/Decrease |
New / Old = 1 ± (percentage/100). | | Unit Rate | Ratio expressed per unit (e.g., ₹5 per kg). | | Applications | - Price & discount - Time‑distance problems
- Mixture & solution problems
- Work & wages | | Tips for TET | - Keep a one‑page “Proportion Formula” cheat sheet.
- Practice cross‑multiplication quickly.
- Avoid unnecessary decimals by keeping fractions. |
3. Worked Example
Problem
A teacher’s salary is ₹12,000 in 2020. It increased by 8% each year. What will be the salary in 2024?
Solution
| Year | Salary | Increase |
|---|---|---|
| 2020 | ₹12,000 | – |
| 2021 | ₹12,000 × 1.08 | 8% |
| 2022 | ₹12,000 × 1.08² | 8% |
| 2023 | ₹12,000 × 1.08³ | 8% |
| 2024 | ₹12,000 × 1.08⁴ | 8% |
Step 1 – Set up the proportion
Salary in 2024 : Salary in 2020 = 1.08⁴ : 1
Step 2 – Compute factor
1.08⁴ ≈ 1.3605 (use a calculator or approximate)
Step 3 – Multiply
Salary2024 = ₹12,000 × 1.3605 ≈ ₹16,326
Answer: ₹16,326 (rounded to nearest rupee)
4. Quick Revision Summary
- Ratio –
A : B→ comparison. - Proportion –
A : B = C : D→ equality of two ratios. - Cross‑Multiplication –
A × D = B × C. - Missing Term –
x = (B × C)/Aorx = (A × D)/C. - Direct & Inverse Proportion – note direction of change.
- Percent Increase/Decrease – use
1 ± (p/100)factor. - Application Areas – price, time, mixture, work, wages.
- TET Strategy – practice quick cross‑multiplication, keep formulas handy, avoid decimals until final step.
Pro tip: For every ratio problem, write the proportion explicitly before doing any arithmetic. This visual step often catches hidden traps (e.g., inverse proportion).
Good luck with your TET preparation!