Ratio & Proportion – IBPS PO Study Notes
(Quantitative Aptitude – IBPS PO)
Why it matters
Ratio & proportion appear in almost every section of the IBPS PO exam: Quantitative Aptitude, Reasoning and Data Interpretation. Mastering this topic gives you a solid base for solving percentage, mixture, profit‑loss, work‑time, speed‑time problems, and many “find what if” type questions.
1. Simple Explanation
| Concept | Definition | Quick Intuition |
|---|---|---|
| Ratio | Two numbers compared with each other, written as (a:b) or (\frac{a}{b}). | “For every a units of one quantity, there are b units of another.” |
| Proportion | An equation of two ratios being equal. For example, ( \frac{a}{b} = \frac{c}{d}). | “If the first ratio equals the second ratio, the quantities are proportionate.” |
| Direct Proportion | When one quantity increases, the other increases in the same proportion. | (y = kx) (k is constant). |
| Inverse Proportion | When one quantity increases, the other decreases while the product remains constant. | (xy = k). |
The key is to express the problem as a proportion and solve for the unknown using cross‑multiplication, or by using the constant of proportionality.
2. Key Points & Formulas
| Topic | Formula / Rule | Notes |
|---|---|---|
| Direct Proportion | ( \frac{a}{b} = \frac{c}{d}) → (ad = bc) | Often used in “work” and “speed” problems. |
| Inverse Proportion | (ab = cd) (or ( \frac{a}{b} = \frac{d}{c})) | Typical in “time vs. workers” or “speed vs. distance” problems. |
| Percentage of a Number | If (p%) of (x) is (y), then ( y = \frac{p}{100} x). | Useful to convert ratios into percentages. |
| Mixture / Weighted Average | (\frac{a\cdot x + b\cdot y}{a+b}) | When mixing two quantities with different qualities. |
| Profit‑Loss | Profit (=) Selling Price – Cost Price. | Use (SP = CP(1 \pm r/100)). |
| Work‑Time | Work = Rate × Time. | For direct proportion: ( \frac{W_1}{W_2} = \frac{T_1}{T_2}). |
| Speed‑Time‑Distance | (S = \frac{D}{T}). | Inverse proportion: (S_1 T_1 = S_2 T_2). |
Common Mistakes to Avoid
- Mixing up direct and inverse proportion – Always check the “product stays constant” vs. “ratio stays constant” condition.
- Forgetting to convert percentages to decimals – e.g., 20% → 0.20.
- Mis‑identifying the knowns – Write down what is given before setting up the proportion.
3. Worked Example
Problem (IBPS‑style)
In a shop, the ratio of pencils to pens sold is 3:5. If the shop sold 240 pens in a day, how many pencils were sold?
Step‑by‑Step
- Identify the ratio – Pencils : Pens = (3:5).
Let pencils = (3x), pens = (5x). - Use the given quantity – Pens sold = 240.
(5x = 240) → (x = \frac{240}{5} = 48). - Find pencils – (3x = 3 \times 48 = 144).
Answer: 144 pencils.
Quick Check
- Ratio ( \frac{144}{240} = \frac{3}{5}) ✔
- Total items = 384, ratio preserved.
4. Quick Revision Checklist
| ✔ | Item | How to Remember |
|---|---|---|
| ✔ | Write down the ratio clearly | Use “a:b” format |
| ✔ | Decide if it's direct or inverse | Look for “product constant” vs. “ratio constant” |
| ✔ | Use cross‑multiplication | (ad = bc) for direct, (ab = cd) for inverse |
| ✔ | Convert percentages to decimals | Divide by 100 |
| ✔ | Check units (time, distance, quantity) | Units must cancel out in proportion |
| ✔ | Verify answer by plugging back | Re‑insert into the ratio |
5. Quick Practice Problems
- Direct Proportion – 8 workers can paint a house in 12 days. How many days will 12 workers take?
- Inverse Proportion – 5 machines produce 200 units in 10 hours. How many units will 8 machines produce in 12 hours?
- Mixture – 4 liters of 30% alcohol solution is mixed with 6 liters of 50% alcohol solution. Find the percentage of alcohol in the final mixture.
- Profit‑Loss – A trader sells a commodity at a 12% profit. If the selling price is ₹13,200, find the cost price.
(Try solving before checking the answer sheet!)
Final Tips for IBPS PO
- Time Management: Ratio & proportion problems usually take 2–3 minutes.
- Quick Cross‑Multiplication: Memorize the rule ( \frac{a}{b} = \frac{c}{d}) → (ad = bc).
- Unit Analysis: If the answer should be “number of items”, ensure the units cancel out.
- Practice Mixed Problems: IBPS often mixes ratio with percentage or profit‑loss in a single question.
Good luck with your preparation! Keep practicing, and ratios will become second nature.