Tamil Nadu Police Sub‑Inspector (SI) – Quantitative Aptitude
Topic: Caselets
Caselets are short real‑life scenarios that test your analytical and numerical skills.
They typically involve a situation (e.g., police operations, traffic, crowd control) and ask you to compute quantities such as time, distance, rate, ratio, profit/loss, or probability.
1. Simple Explanation
| Element | What it means |
|---|---|
| Scenario | A narrative that sets the context (e.g., “An officer has to escort a suspect through a busy street”). |
| Data | Numerical values given in the problem (distances, speeds, numbers of people, rates of change). |
| Question | A direct request, usually “Find X” (time, distance, total cost, etc.). |
| Logic | Apply relevant formulas (speed = distance/time, ratio–proportion, simple/compound interest, area/volume, probability). |
Tip: Treat each caselet as a mini‑story. Identify what you need to find, list the given facts, and choose the appropriate formula.
2. Key Points to Remember
| # | Point | Why it matters |
|---|---|---|
| 1 | Read the whole problem first | Avoid missing hidden assumptions (e.g., “while he is walking” -> speed of walking). |
| 2 | Convert units early | 1 km = 1000 m, 1 hour = 60 min. Unit consistency prevents errors. |
| 3 | Break complex problems into sub‑problems | Solve each part, then combine results. |
| 4 | Use proportional reasoning | Many caselets involve ratios (e.g., “2:3” ratio of police to civilians). |
| 5 | Check for “inclusive/exclusive” wording | “More than 10” vs “at least 10”. |
| 6 | Verify results | If the answer is a number that seems too large/small, double‑check. |
| 7 | Time management | Allocate 2–3 minutes per caselet; keep a fast, systematic approach. |
3. Worked Example
Caselet
A traffic police officer must escort a suspect across a 2 km stretch of road.
• The officer walks at 5 km/h.
• The suspect walks at 4 km/h.
• The officer meets a moving vehicle traveling at 30 km/h from the opposite direction at a point 0.5 km from the start.
Q1: How long will it take for the officer and suspect to reach the destination?
Q2: If the officer stops to check the vehicle and this takes 5 minutes, what is the total time spent?
Step‑by‑Step Solution
Q1 – Time to reach destination
-
Relative speed of officer and suspect
- Officer speed = 5 km/h
- Suspect speed = 4 km/h
- Relative speed (moving together) = 5 km/h (since they move in the same direction, the officer is only 1 km/h faster).
-
Effective distance to cover
- Total distance = 2 km
- They start together, so distance to cover = 2 km.
-
Time = Distance ÷ Speed
[ t = \frac{2\ \text{km}}{5\ \text{km/h}} = 0.4\ \text{h} = 24\ \text{min} ]
Answer Q1: 24 minutes.
Q2 – Total time including stop
-
Stop time = 5 min.
-
Total time = 24 min + 5 min = 29 min.
Answer Q2: 29 minutes.
Quick Check
- Speed difference: 1 km/h → 24 min for 2 km → plausible.
- Stop: 5 min added → 29 min total → within the typical time limit.
4. Quick Revision Summary
| Concept | Formula | Typical Use in Caselets |
|---|---|---|
| Speed, Distance, Time | (v = d/t) or (t = d/v) | Walking, driving, moving vehicles |
| Relative Speed | (v_{\text{rel}} = v_1 \pm v_2) | Two moving objects in same/opposite directions |
| Ratio–Proportion | (a:b = c:d) → (d = \frac{b \cdot c}{a}) | Police to civilian ratio, resource allocation |
| Simple Interest | (I = PRT) | Compensation, fines |
| Compound Interest | (A = P(1 + r)^t) | Loan amortization |
| Area/Volume | (A_{\text{rect}} = l \times w), (V_{\text{cube}} = s^3) | Room layout, crowd density |
| Probability | (P = \frac{\text{favourable outcomes}}{\text{total outcomes}}) | Chance of an event (e.g., suspect escape) |
Practice Tips
- Draw a quick diagram – helps visualize distances and directions.
- Write down all given numbers – avoid forgetting a key piece of data.
- Label your variables – e.g., (d) for distance, (t) for time, (v) for speed.
- Use shortcuts – e.g., if speed is in km/h and distance in km, time comes out in hours directly.
- Cross‑check – if your time seems > 30 minutes for a 2 km walk, re‑calculate.
5. Final Quick Revision Checklist
- Read the problem once fully.
- Identify what is asked.
- List given data and units.
- Choose the right formula.
- Compute, checking units.
- Add any additional actions (e.g., stops, delays).
- Verify plausibility (time, distance, speed).
Remember: Caselets test application of basic formulas in realistic police scenarios. Keep your calculations clean, units consistent, and your reasoning logical. Good luck!