Karnataka Police Constable – Quantitative Aptitude
Time – Speed – Distance
Objective – Solve everyday problems involving motion of a vehicle, person, or any object.
Key Idea – All three variables are related by a simple proportionality.
1. Simple Explanation
| Variable | Symbol | Unit | What it represents |
|---|---|---|---|
| Distance | (d) | km, m, ft, etc. | Path traveled |
| Speed (or Velocity) | (v) | km/h, m/s, ft/min, etc. | Rate of travel |
| Time | (t) | h, min, s, etc. | Duration of travel |
Core Relationship
[ \boxed{d = v \times t} ]
- Distance = Speed × Time
- Rearrange to find any missing variable:
- (v = \dfrac{d}{t})
- (t = \dfrac{d}{v})
2. Key Points to Remember
| # | Point | Why It Matters |
|---|---|---|
| 1 | Units must match | Before multiplying/dividing, convert all lengths to km (or meters) and times to hours (or seconds). |
| 2 | Speed vs Velocity | In these questions only magnitude (speed) matters; direction is ignored. |
| 3 | Average speed | If distance isn’t uniform (e.g., stops, turns), use average speed: total distance ÷ total time. |
| 4 | Multiple segments | For a journey comprising different speeds, compute distance for each segment and sum. |
| 5 | Common conversions | 60 min = 1 h, 1000 m = 1 km, 1 mph ≈ 1.609 km/h (not needed for most exams). |
| 6 | Common trap | Adding speeds instead of distances when you have same time. |
| 7 | Check reasonableness | e.g., 10 km in 0.5 h → 20 km/h – plausible for a bus. |
3. Worked Example
Problem
A police patrol car travels 120 km from City A to City B.
The first 80 km it travels at 60 km/h.
The remaining 40 km it travels at 45 km/h.
Question: What is the average speed of the car for the whole journey?
Step‑by‑Step
-
Compute time for each segment
[ t_1 = \frac{d_1}{v_1} = \frac{80}{60} = 1.\overline{3}\text{ h} ] [ t_2 = \frac{d_2}{v_2} = \frac{40}{45} = 0.\overline{8}\text{ h} ]
-
Total time
[ t_{\text{total}} = t_1 + t_2 = 1.\overline{3} + 0.\overline{8} = 2.1\text{ h} ] (Rounded to one decimal place; you can keep more digits if needed.)
-
Total distance
[ d_{\text{total}} = 80 + 40 = 120\text{ km} ]
-
Average speed
[ v_{\text{avg}} = \frac{d_{\text{total}}}{t_{\text{total}}} = \frac{120}{2.1} \approx 57.14\text{ km/h} ]
Answer: ≈ 57 km/h (to nearest km/h).
Quick Check
- 57 km/h for 2.1 h → (57 \times 2.1 \approx 119.7) km, close to 120 km.
- Reasonable: between 45 and 60 km/h.
4. Quick Revision Summary
| Concept | Formula | Example Use |
|---|---|---|
| Distance | (d = v \times t) | Find distance of a train traveling 80 km/h for 1.5 h → 120 km |
| Speed | (v = \dfrac{d}{t}) | Determine speed of a bike covering 30 km in 0.5 h → 60 km/h |
| Time | (t = \dfrac{d}{v}) | Time taken for a 150 km drive at 50 km/h → 3 h |
| Average Speed | (v_{\text{avg}} = \dfrac{\text{Total Distance}}{\text{Total Time}}) | Two‑segment journey: 80 km at 60 km/h + 40 km at 45 km/h → 57 km/h |
| Multiple Segments | Sum distances, sum times, then compute average | Useful for mixed terrain or traffic conditions |
| Unit Checking | Convert all lengths to km, times to hours | Avoids “km/min” or “h/km” mistakes |
Tips for Exam Day
- Read carefully – identify which variable is missing.
- Convert units early – eliminates later confusion.
- Use fraction form – keeps accuracy when adding times.
- Rough mental check – ensure the answer lies between the extreme speeds.
- Write down each step – reduces chances of arithmetic slip‑ups.
Good luck! Mastering the time‑speed‑distance relationship will give you confidence in tackling any quantitative problem in the Karnataka Police Constable exam.