📚 Quantitative Aptitude – Caselets
Program: Puducherry Patwari / Lekhpal
Section: Quantitative Aptitude
Topic: Caselets
Caselets are short, real‑life based problems that test quick reasoning, basic algebra, and mental math.
They appear in many competitive exams (including the Patwari/Lekhpal exam) and are usually 10–15 questions per paper, each worth 1–2 marks.
1. Simple Explanation
| Feature | What it means |
|---|---|
| Length | 1–3 sentences describing a scenario (salary, profit, distance, mixture etc.) |
| Goal | Find a numerical answer (age, percentage, time, quantity, etc.) |
| Difficulty | Requires setting up a simple equation or using a known proportionality |
| Time | Usually 1–2 minutes each – must be solved quickly |
Example: “A shopkeeper sold 60% of his stock at ₹20 each and the rest at ₹25 each. If the total profit was ₹1,200, how many items were sold?”
2. Key Points & Tips
| # | Key Point | Why it matters | Quick Tip |
|---|---|---|---|
| 1 | Identify the unknown | Pinpoint what you’re asked to find | Write “Unknown = ______” early |
| 2 | Look for ratios & percentages | Many caselets use percentages (e.g., 50% of something) | Convert percentages to decimals (50% = 0.5) before multiplying |
| 3 | Set up a single equation | Keeps it simple and reduces errors | Use “Let X = …” then write the total in terms of X |
| 4 | Use elimination/ substitution | Helps when two equations are given | Solve one equation for a variable, substitute in the other |
| 5 | Check units | Avoids mistakes (km/h, Rs., days, etc.) | Keep track of the units in each term |
| 6 | Round only at the end | Prevents cumulative rounding errors | Keep numbers exact until the final step |
| 7 | Time‑management | 5–10 min for 10‑15 questions | 30 s per question; if stuck, move on and circle back |
| 8 | Common patterns | • Profit & Loss • Speed, Distance, Time • Mixture & Dilution • Age & Time • Work & Labour • Simple Interest & Compound Interest |
Memorize the standard formulas for each pattern |
| 9 | Use mental math tricks | Saves time | • Multiplying by 5 → divide by 2 then × 10 • 9×N = 10N – N • Adding 100 to a number and subtracting 1 gives 99×N + 1 |
| 10 | Practice with timed mock tests | Builds speed and accuracy | 5–10 min mock test every week |
3. Worked Example
Caselet
"Ms. Ramesh runs a bakery. She sells 40% of her cakes at ₹60 each and the rest at ₹80 each. If she made a total profit of ₹4,800, how many cakes did she sell in total?"
Step‑by‑Step Solution
-
Let
- Total cakes sold = (C)
- Profit per cake at ₹60 = (P_1)
- Profit per cake at ₹80 = (P_2)
-
Assumption – Suppose the cost price per cake is (x) rupees (same for all).
- Profit per cake at ₹60 = (60 - x)
- Profit per cake at ₹80 = (80 - x)
-
Breakdown of sales
- Cakes sold at ₹60 = (0.4C)
- Cakes sold at ₹80 = (0.6C)
-
Total profit
[ \text{Profit} = (0.4C)(60 - x) + (0.6C)(80 - x) ] Given Profit = ₹4,800. -
Solve for (x)
Expand: [ 0.4C(60 - x) + 0.6C(80 - x) = 4800 ] [ 24C - 0.4Cx + 48C - 0.6Cx = 4800 ] [ 72C - Cx = 4800 ] [ Cx = 72C - 4800 ] [ x = 72 - \frac{4800}{C} ]Since (x) must be positive, we need a value of (C) that satisfies this.
We can also treat (C) as the unknown and solve directly:[ 72C - Cx = 4800 ] But we also have (x = 60 - \frac{4800}{0.4C}) (from profit at ₹60).
This approach becomes messy; instead, use a simpler method