Karnataka Police Sub‑Inspector (SI) – Quantitative Aptitude
Topic: Caselets
Caselets are short, real‑world scenarios that test your ability to interpret data, make logical deductions, and compute quickly.
They are normally 2–3 lines long and require you to solve a problem in a limited time (often 30–40 seconds).
1. Simple Explanation
| What are Caselets? | Why they matter? |
|---|---|
| A concise narrative that presents a numerical problem (e.g., “In a village 30 % of 200 houses are double‑storey…”) | They mimic real‑world police work: quick decision‑making with incomplete data. |
| Usually 1–2 questions, each worth 1–2 marks. | They test reasoning, arithmetic, and time‑management skills. |
2. Key Points
| # | Concept | How to Approach |
|---|---|---|
| 1. Read the whole statement first | One pass to understand the problem. | |
| 2. Identify the question clearly | Look for words like find, calculate, what is the ratio, which one is true. | |
| 3. Spot the given data and units | Make a quick list or table. | |
| 4. Translate words into formulas | Percentages → p/100 × value, ratios → a:b = a/b, averages → sum ÷ n. | |
| 5. Do quick mental math or use scratch paper | Avoid long multiplication; use estimation when appropriate. | |
| 6. Double‑check the answer’s plausibility | Does it fit the context? Is it a whole number when expected? | |
| 7. Keep a “time‑buffer” | Aim to finish each caselet in ~30 seconds. |
3. Worked Example 1 – Percentage & Ratio
Caselet
In a police station, 40 % of 400 cases are solved within 5 days. The remaining cases are solved in 10 days. If the average days taken for all cases is 7 days, how many cases were solved in 10 days?
Step‑by‑Step
| Step | Action | Calculation | Result |
|---|---|---|---|
| 1 | Compute solved in 5 days | 40 % of 400 = 0.40 × 400 = 160 cases | 160 |
| 2 | Remaining cases | 400 – 160 = 240 cases | 240 |
| 3 | Let (x) be cases solved in 10 days. | Total days = 160×5 + x×10 = 2000 + 10x | |
| 4 | Average days = 7 → total days = 7×400 = 2800 | 2800 | |
| 5 | Solve for (x) | 2000 + 10x = 2800 → 10x = 800 → (x = 80) | 80 |
Answer: 80 cases were solved in 10 days.
4. Worked Example 2 – Speed & Distance
Caselet
Two officers, A and B, start from the same point. A travels at 30 km/h, B at 20 km/h. They meet after 2 hours. How far from the start did they meet?
Step‑by‑Step
| Step | Action | Calculation | Result |
|---|---|---|---|
| 1 | Distance covered by A | 30 km/h × 2 h = 60 km | 60 |
| 2 | Distance covered by B | 20 km/h × 2 h = 40 km | 40 |
| 3 | Total distance from start to meeting point | Since both start together, the meeting point is 60 km from start (distance of the faster officer). | 60 km |
Answer: They met at 60 km from the start.
5. Quick Revision Summary
- Read fully & locate the question
- List data & units
- Translate words → formulas
- Use mental math & scratch paper
- Check plausibility (whole number, sense‑making)
- Finish within ~30 s per caselet
Quick Flashcards (Optional)
| Flashcard | Question | Answer |
|---|---|---|
| 1 | A caselet gives 30 % of 200 houses are double‑storey. How many are single‑storey? | 140 |
| 2 | Two officers cover 45 km and 30 km in 3 h. What’s their average speed? | (45+30)/3 = 25 km/h |
| 3 | 120 cases solved: 50 % on day 1, rest on day 2. Avg days = 1.5. How many solved on day 2? | 60 |
Tip for Practice:
- Time yourself for each caselet.
- After solving, quickly recalculate to ensure accuracy.
- Keep a notebook of frequently used shortcut tricks (e.g., “p% of x = x × p / 100”).
Good luck with your preparation!