📚 Odisha Patwari / Lekhpal – Quantitative Aptitude
Topic: Caselets
Caselet – a short paragraph or scenario that contains numbers and facts.
The task is to read it carefully, pick out the relevant data and solve the numerical question(s) that follow.
1️⃣ Simple Explanation
| What is a caselet? | Why it matters |
|---|---|
| A concise real‑life situation written in plain language | Tests reading comprehension + mathematics simultaneously |
| Usually 1–3 sentences long | Requires quick extraction of key numbers |
| Questions can involve any topic: wages, travel, shop, percentages, ratios, etc. | Helps you practice time‑management – you’ll see it in the exam! |
Goal:
- Extract the facts (numbers, relationships).
- Translate them into a mathematical expression or equation.
- Solve and check if the answer makes sense.
2️⃣ Key Points & Checklist
| # | Key Point | How to Apply |
|---|---|---|
| 1 | Read once, mark | Read the whole paragraph once, underline or circle numbers, keywords (e.g., per day, increase by, share, total, difference). |
| 2 | Identify the question | Highlight the exact query – “how much?”, “what is the rate?”, “difference between A and B?” |
| 3 | Choose the right formula | Common patterns: (\text{Rate} = \frac{\text{Cost}}{\text{Quantity}}), (\text{Percent} = \frac{\text{Part}}{\text{Whole}}\times100), (\text{Simple interest} = P\times R\times T). |
| 4 | Set up equations | Write a single equation or system if multiple unknowns. |
| 5 | Solve step‑by‑step | Keep track of units, do the arithmetic carefully. |
| 6 | Check plausibility | Roughly estimate to see if the answer is reasonable. |
| 7 | Time‑practice | Aim to finish a caselet in 1–1.5 minutes. |
Tip: Keep a mini‑cheat‑sheet of formulas handy for quick reference.
3️⃣ Common Caselet Patterns
| Pattern | Typical Question | Sample Formula |
|---|---|---|
| Equation with two unknowns | “If 5 workers complete a job in 12 days, how many days will 8 workers take?” | ( \frac{W}{D_1} = \frac{W}{D_2} ) → (D_2 = D_1 \times \frac{8}{5}) |
| Percentage change | “A shopkeeper’s profit increased by 15%, now he earns Rs. 300.” | ( \text{Profit} = \text{Cost} \times (1 + \frac{p}{100}) ) |
| Time‑distance | “A train covers 120 km in 3 hours. How long will it take to cover 200 km at same speed?” | ( \text{Speed} = \frac{120}{3} = 40 \text{ km/h} ) → (t = \frac{200}{40}) |
| Simple interest | “He deposited Rs. 5000 at 6% per annum for 2 years. What is the interest?” | (I = P \times R \times T) |
| Compound interest | “Rs. 10,000 is invested at 10% per annum compounded yearly for 3 years.” | (A = P (1 + r)^n) |
| Ratios & proportions | “The ratio of boys to girls in a class is 3:4. If there are 28 girls, how many boys?” | ( \frac{B}{G} = \frac{3}{4} ) → ( B = \frac{3}{4}\times28 ) |
| Profit‑loss | “A trader’s cost price is Rs. 200, he sells at 20% profit. What is the selling price?” | (SP = CP \times (1 + \frac{p}{100})) |
4️⃣ Worked Example
Caselet
“A farmer sold 60 kg of rice in the market. He kept 10% of the total weight as a reserve. The remaining rice was sold at Rs. 30 per kg. How much money did he earn from the sale?”
Step‑by‑Step Solution
| Step | Action | Calculation |
|---|---|---|
| 1 | Read & mark | Total weight = 60 kg, reserve = 10%, selling price = Rs.30/kg |
| 2 | Find reserve weight | (10% \text{ of } 60 = 0.10 \times 60 = 6) kg |
| 3 | Compute sellable weight | (60 - 6 = 54) kg |
| 4 | Calculate earnings | (54 \text{ kg} \times 30 \text{ Rs/kg} = 1620) Rs |
| 5 | Answer | Rs. 1,620 |
Quick sanity check – 60 kg at Rs.30/kg would give Rs.1,800; subtracting 10% of weight (5% of total price) ≈ Rs.180 → Rs.1,620. ✔️
5️⃣ Quick Revision Summary
| Concept | Formula | Quick Cue |
|---|---|---|
| Rate | (R = \frac{C}{Q}) | Cost ÷ Quantity |
| Percent | (P = \frac{Part}{Whole}\times |