Quantitative Aptitude – Caselets
For Nagaland Police Constable (NPSC) Examination
Caselets are concise problem‑solving questions that test your ability to apply basic mathematical concepts under time pressure. They usually involve a short narrative and require you to deduce the answer by using arithmetic, algebra, ratios, percentages, time‑distance, and sometimes logic or reasoning.
1. Simple Explanation
| Aspect | What It Means | Why It Matters |
|---|---|---|
| Definition | A caselet is a brief, real‑life problem (often 4–6 lines) that demands quick calculations or reasoning. | They cover a wide range of topics in a single question, so you must be flexible. |
| Structure | 1. Scenario – a story or situation. 2. Data – numbers, rates, times. 3. Question – what needs to be found. |
Helps you practice reading comprehension along with math. |
| Answer | Usually a single integer, a fraction, or a short expression (e.g., “$75$ km”, “$12$ days”). | Speed & accuracy are key; avoid unnecessary steps. |
2. Key Points to Master
| Topic | Typical Formulas / Concepts | Quick Tips |
|---|---|---|
| Ratios & Proportions | ( \frac{a}{b} = \frac{c}{d} ) → ( c = \frac{a \times d}{b} ) | Keep the ratio in lowest terms; cross‑multiply directly. |
| Percentage | ( \text{Percent} = \frac{\text{part}}{\text{whole}} \times 100 ) | Remember “× 100 ÷ whole” or “× 1 %” tricks. |
| Simple Interest | ( SI = \frac{P \times R \times T}{100} ) | Plug in values directly; watch units. |
| Compound Interest | ( A = P \bigl(1 + \frac{r}{n}\bigr)^{nt} ) | For quick answers, use approximate formulas or log tables. |
| Time‑Distance | ( \text{Time} = \frac{\text{Distance}}{\text{Speed}} ) | Convert units first (km/h → min/km). |
| Mixture / Work | ( \text{Total Time} = \frac{\text{Total Work}}{\text{Rate}} ) | For work problems, use “rate per time” and LCM of denominators. |
| Algebraic Equations | Linear equations, simultaneous equations | Write equations in simplest form; solve by substitution or elimination. |
| Logic/Reasoning | Deductive statements, conditionals | Translate words into symbolic form (e.g., “if A then B”). |
| Units & Conversion | 1 km = 1000 m; 60 min = 1 h | Keep track of units; convert before calculation. |
3. Worked Example
Caselet
Problem
A police team of 12 officers is assigned to cover a road of length 45 km. The first 8 officers are sent on a patrol at a speed of 60 km/h. The remaining 4 officers start 15 minutes later, moving at 48 km/h.
Question: At what time will the entire team finish the patrol?
Step–by–Step Solution
| Step | Explanation | Calculation |
|---|---|---|
| 1. Convert the delay to hours | 15 minutes = 0.25 h | – |
| 2. Find time for the first group | (t_1 = \frac{45,\text{km}}{60,\text{km/h}} = 0.75,\text{h}) | (t_1 = 0.75) h |
| 3. Find time for the second group | (t_2 = \frac{45}{48} = 0.9375,\text{h}) | (t_2 = 0.9375) h |
| 4. Add the delay for the second group | (T_2 = t_2 + 0.25 = 1.1875,\text{h}) | (T_2 = 1.1875) h |
| 5. Determine overall finish time | The team finishes when the slowest group finishes → (T_{\text{overall}} = 1.1875) h | (T_{\text{overall}} = 1.1875) h |
| 6. Convert to hours:minutes | 0.1875 h = 0.1875 × 60 min = 11.25 min ≈ 11 min 15 sec | Answer: 1 h 11 min 15 sec |
Result: The entire team finishes the patrol at 1 hour 11 minutes 15 seconds after the first group starts.
4. Quick Revision Summary
- Read carefully – identify the scenario, data, and what is asked.
- List known values – write them in a table or bullet list.
- Choose the relevant formula – ratios, percentages, interest, time‑distance, algebra, or logic.
- Check units – convert to common units before computing.
- Cross‑multiply for ratios; add/subtract for linear equations.
- Round only at the end – avoid early rounding errors.
- Verify – ensure the answer makes sense in context (e.g., positive time, realistic speed).
| Technique | How to Use |
|---|---|
| Cross‑Check | After solving, plug the answer back into the original problem. |
| Estimate First | Rough estimate to confirm if the final answer is plausible. |
| Keep it Simple | Use the most straightforward formula; avoid unnecessary steps. |
| Time Management | Allocate about 1–2 minutes per caselet; practice speed. |
Practice Tip
Create a mini‑caselet for yourself every