📚 Odisha Forest Guard – Quantitative Aptitude
🚀 Time – Speed – Distance (TSD)
Goal: Master the basic relationship between Time (T), Speed (S) and Distance (D) so you can solve any TSD problem in under 30 seconds.
1️⃣ Simple Explanation
| Symbol | Meaning | Unit |
|---|---|---|
| T | Time taken | Hours (h), Minutes (min), Seconds (s) |
| S | Speed (rate of travel) | Kilometres per hour (km/h) or Miles per hour (mph) |
| D | Distance covered | Kilometres (km) or Miles (mi) |
The Core Formula
[ \boxed{D = S \times T} ]
- Distance = Speed × Time
- Re‑arrange to find any missing quantity:
- ( S = \frac{D}{T} )
- ( T = \frac{D}{S} )
Tip: Always keep units consistent (e.g., convert minutes to hours before plugging into the formula).
2️⃣ Key Points & Tricks
| Point | Description | Why It Matters |
|---|---|---|
| 2.1. Unit Consistency | Convert minutes → hours (divide by 60), seconds → hours (divide by 3600). | Prevents wrong answers. |
| 2.2. Speed vs. Velocity | Speed is scalar (magnitude only). Velocity includes direction. | In most exam problems, only speed is required. |
| 2.3. Average Speed | When distance is split into segments with different speeds, use total distance / total time. | Avoids calculating each segment separately. |
| 2.4. Relative Speed | If two objects move towards/away from each other, combine speeds: (S_{\text{relative}} = S_1 \pm S_2). | Useful for “meeting” or “passing” problems. |
| 2.5. Ratios & Proportional Reasoning | Sometimes only a ratio is needed (e.g., “time taken by A is 3 times that of B”). | Speeds may cancel out. |
| 2.6. Common Pitfall | Mixing up “speed” and “velocity”; forgetting to convert units. | Leads to systematic mistakes. |
3️⃣ Worked Example
Problem
A forest guard walks from his post to a forest clearing. The distance is 12 km. He walks at a constant speed of 4 km/h. How long will it take him to reach the clearing? And if he returns at 6 km/h, how much total time will he spend on this round trip?
Step‑by‑Step
| Step | Explanation | Calculation |
|---|---|---|
| 1. Convert speed to consistent units | Already in km/h, so OK. | – |
| 2. Find time to reach clearing | (T = D / S) | (T_{\text{out}} = 12 / 4 = 3) h |
| 3. Find return time | (T_{\text{back}} = 12 / 6 = 2) h | |
| 4. Total time | Add both legs | (T_{\text{total}} = 3 + 2 = 5) h |
Answer:
- Outward journey: 3 hours.
- Return journey: 2 hours.
- Total round‑trip time: 5 hours.
Quick sanity check: Faster speed on the return leg makes sense because 6 km/h > 4 km/h, so the return takes less time.
Extra: Using Average Speed
If the guard had to go and come back in one continuous trip at different speeds, we could also compute average speed:
[ S_{\text{avg}} = \frac{\text{Total distance}}{\text{Total time}} = \frac{24}{5} = 4.8 \text{ km/h} ]
4️⃣ Quick Revision Summary
| Concept | Formula | Example |
|---|---|---|
| Distance | (D = S \times T) | 4 km/h × 3 h = 12 km |
| Speed | (S = D / T) | 12 km / 3 h = 4 km/h |
| Time | (T = D / S) | 12 km / 4 km/h = 3 h |
| Average Speed | (S_{\text{avg}} = \frac{D_{\text{total}}}{T_{\text{total}}}) | 24 km / 5 h = 4.8 km/h |
| Relative Speed | (S_{\text{rel}} = S_1 \pm S_2) | Two trains 80 km/h & 60 km/h → 140 km/h when moving towards each other |
| Unit Conversion | 1 h = 60 min; 1 h = 3600 s | 30 min = 0.5 h |
Quick Tip: For every problem, write down what you need (D, S, or T) and what you know; then pick the correct formula.
Remember: Keep all units the same → no surprises.
5️⃣ Practice Question (Try It)
*A forest guard drives a jeep from Station A to Station B, 90 km apart, at an average speed of 30 km/h. On the return trip, he drives at 45 km/h.
- How long did each leg take?
- What was his average speed for the whole round trip?*
(Answer in the next page!)
🎯 Final Words
Mastering TSD is all about unit consistency and selecting the right formula. Once you get these three, you can solve any related problem in a flash. Good luck with your Odisha Forest Guard exam!