📚 Quantitative Aptitude – Caselets
Study Notes for RHCSA Candidates (and anyone preparing for competitive exams)
1. What Are Caselets?
| 📌 Definition |
|---|
| Caselets are short, narrative‑style problems that mimic real‑world scenarios. They combine multiple quantitative concepts (e.g., ratios, percentages, time‑speed, profit‑loss, compound interest) into a single question. |
- They test application and analytical skills, not just rote formulas.
- Usually 3–5 lines of story, followed by one or more sub‑questions.
- Common in exams like JEE‑Main, JEE‑Advanced, CAT, GMAT, IES, and many civil‑services tests.
2. Key Points to Master
| 🔑 Point | Why It Matters | Quick Tip |
|---|---|---|
| 1. Read Carefully | Mis‑reading the story can lead to wrong assumptions. | Read once fast, then read again while highlighting numbers. |
| 2. Identify Variables | Convert words into symbols: x = total, y = part, k = rate, etc. | Write a short “Equation Sheet” next to the problem. |
| 3. Choose the Right Formula | A caselet may involve ratios, percentages, or time‑distance relationships. | Keep a cheat‑sheet of common formulas (e.g., Time = Distance / Speed, Profit% = (Profit / Cost) × 100). |
| 4. Break Down into Sub‑Problems | Complex stories often hide multiple independent equations. | Create a flow‑chart or diagram to link variables. |
| 5. Check Units & Consistency | Mixing units (km/h with m/min) throws off calculations. | Convert everything to a common unit before solving. |
| 6. Verify with a Quick Estimate | A sanity check prevents arithmetic errors. | Round numbers to nearest 10 or 100 and see if the result is plausible. |
| 7. Practice Time Management | Caselets are usually longer; time can be a limiting factor. | Aim to solve a caselet in <5 min once you’re comfortable. |
3. Worked Example
Caselet:
Three workers, A, B, and C, can complete a construction job in 18, 24, and 30 days respectively. They start working together on Day 1. After 5 days, A leaves the job. How many additional days will B and C need to finish the remaining work?
Step‑by‑Step Solution
| Step | What to Do | Calculation |
|---|---|---|
| 1. Convert rates to “work per day” | (R_A = 1/18), (R_B = 1/24), (R_C = 1/30) | |
| 2. Work done in first 5 days (all three) | (W_1 = 5 \times (R_A + R_B + R_C)) | (W_1 = 5 \times \left(\frac{1}{18}+\frac{1}{24}+\frac{1}{30}\right) = 5 \times \frac{1}{9} = \frac{5}{9}) |
| 3. Remaining work | (W_{\text{rem}} = 1 - W_1) | (W_{\text{rem}} = 1 - \frac{5}{9} = \frac{4}{9}) |
| 4. Combined rate of B & C | (R_{BC} = R_B + R_C = \frac{1}{24} + \frac{1}{30}) | (R_{BC} = \frac{5+4}{120} = \frac{9}{120} = \frac{3}{40}) |
| 5. Time for B & C to finish | (t = \frac{W_{\text{rem}}}{R_{BC}}) | (t = \frac{4/9}{3/40} = \frac{4}{9} \times \frac{40}{3} = \frac{160}{27} \approx 5.93) days |
Answer: ~ 5.9 days (≈ 6 days) for B and C to finish.
4. Quick Revision Summary
| ✅ Concept | ✅ Formula | ✅ Example |
|---|---|---|
| Ratios | (a:b = x:y) → (a = \frac{x}{x+y} \times \text{Total}) | 3:5 ratio → 3/(3+5)=3/8 of total |
| Percentages | (%\text{Change} = \frac{\text{Change}}{\text{Base}}\times100) | 20% increase → (1.20 \times) base |
| Time‑Speed‑Distance | (t = \frac{d}{v}), (d = vt) | 60 km in 2 h → (v=30) km/h |
| Profit–Loss | (\text{Profit}% = \frac{\text{Profit}}{\text{Cost}}\times100) | Cost 200, sell 240 → 20% profit |
| Compound Interest | (A = P(1+r/n)^{nt}) | P=1000, r=5%, n=1, t=3 → A=1157.63 |
| Work Problems | Work done = Rate × Time | Rate=1/12 job/day, Time=6 → 0.5 job |
5. Practice Tips
- Create Your Own Caselets – Write 3‑line stories and solve them.
- Timed Drills – Use a timer; aim to finish 3–5 caselets in 15 min.
- Peer Review – Exchange solutions to spot common pitfalls.
- Use Diagrams – For multi‑variable stories, a quick sketch can