Ratio & Proportion – SBI Clerk Study Notes
Why it matters for the SBI Clerk exam
The “Ratio & Proportion” section tests your ability to handle relative comparisons, scaling, and proportionate relationships – skills needed in finance, accountancy, and general business scenarios.
1. Simple Explanation
| Concept | What it means | Everyday example |
|---|---|---|
| Ratio | A comparison of two quantities expressed as a:b or a/b. |
If a shop sells 3 apples for ₹10, the ratio of apples to price is 3 : 10. |
| Proportion | An equation stating that two ratios are equal, i.e. a:b = c:d. |
If 4 pens cost ₹12, then 5 pens cost ? → set up proportion 4/12 = 5/x. |
| Direct Proportion | When one quantity increases, another increases in the same proportion. y = kx. |
Speed vs. distance: 60 km/h → 120 km in 2 hrs. |
| Inverse Proportion | When one quantity increases, the other decreases proportionally. y = k/x. |
4 workers finish a job in 5 days → 8 workers finish in ? days: 4×5 = 8×?. |
2. Key Points & Formulas
| Topic | Formula / Rule | Notes |
|---|---|---|
| Basic Ratios | a : b or a / b |
Write as a fraction to simplify. |
| Simplifying Ratios | Divide both terms by GCD. | 18 : 24 → 3 : 4 (divide by 6). |
| Cross‑Multiplication | If a:b = c:d, then a·d = b·c. |
Quick way to solve for unknowns. |
| Direct Proportion | y = kx. k = y/x |
Use when y/x is constant. |
| Inverse Proportion | y = k/x. k = y·x |
Use when y·x is constant. |
| Percent of a Ratio | If a:b = 1:4, then a is 20 % of b. |
a = (20/100)·b. |
| Scaling Ratios | Multiply or divide both terms by same number. | Keeps ratio unchanged. |
| Compound Proportion | a:b = c:d = e:f. a·d·f = b·c·e |
Useful for multi‑step proportion. |
| Mixture / Weighted Average | Total = (sum of part × weight) / sum of weights. |
Classic mixture problem. |
| Percentage Increase/Decrease | % change = (new – old) / old × 100. |
Can be expressed as a ratio. |
3. Worked Example
Problem
A company produces 200 units of Product A in 5 days.
If production is increased to 300 units, how many days will it take provided the rate of production remains constant?
Step‑by‑Step Solution
-
Identify the relationship
- Production rate is directly proportional to the number of units produced and inversely proportional to time.
- We can use the direct proportion formula:
[ \frac{\text{Units}}{\text{Time}} = \text{Rate} ]
-
Compute the rate
[ \text{Rate} = \frac{200 \text{ units}}{5 \text{ days}} = 40 \text{ units/day} ] -
Set up proportion for new scenario
[ \frac{300 \text{ units}}{x \text{ days}} = 40 \text{ units/day} ] -
Solve for (x)
[ 300 = 40x ;;\Longrightarrow;; x = \frac{300}{40} = 7.5 \text{ days} ]
Answer: It will take 7.5 days to produce 300 units at the same rate.
Quick Cross‑Multiplication Check
Set up 200 : 5 = 300 : x → 200x = 5·300 → 200x = 1500 → x = 7.5. Same result.
4. Quick Revision Summary
| Concept | Key Take‑away |
|---|---|
| Write ratios as fractions | Easier to simplify and cross‑multiply. |
| Simplify first | Reduce to lowest terms before working. |
| Cross‑multiply | Quick method for any proportion. |
| Direct proportion | y/x is constant. |
| Inverse proportion | y·x is constant. |
| Scale ratios | Multiply or divide both terms by the same number. |
| Check units | Ensure consistency (e.g., units/day). |
| Common pitfalls | Forgetting to convert percentages to decimals, mixing up direct vs. inverse proportions, not simplifying ratios. |
Quick Practice Questions
- If 6 pens cost ₹30, how much will 10 pens cost?
- A machine can produce 120 units in 4 hours. How many units can it produce in 7 hours?
- The ratio of boys to girls in a class is
3:5. If there are 48 students, how many girls are there? - A recipe calls for 2 cups of flour for every 3 cups of sugar. If you have 9 cups of sugar, how many cups of flour are needed?
Try solving them using the rules above, then check your answers with cross‑multiplication.
Final Tips for SBI Clerk
- Practice mental math: Many ratio problems can be solved quickly by mental simplification.
- Time management: Allocate 1–2 minutes per problem; skip if stuck, return later if time permits.
- Check for hidden inverses: If the problem mentions “more workers → less time,”