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RRB NTPC Preparation Series: Part 5 - Time & Distance in Maths (Full Detailed Explanation with High-Quality Content)
Friends! Ee RRB NTPC 2025 preparation series lo Part 5 ki vacham, topic "Time & Distance" meeda. Idi Maths lo super high weightage chapter –
- CBT 1 lo 2-4 questions (7-13% weightage),
- CBT 2 lo 3-5 questions (9-14% weightage),
- Total Maths lo ~25% questions (with Time & Work, Interest, Percentage combine).
2025 Update (Oct 28): RRB UG notification live – total vacancies 11,910. Time & Distance lo relative speed, trains crossing platforms, boats & streams, average speed, circular track ekkuva vastunnayi. Exam Jan-Feb 2026.
- Formulas (18+)
- Shortcuts (10+)
- Examples (6 NTPC level)
- Practice (14 graded)
- Integration with Part 1-4
- 2025-specific strategy
Next Part 6: Ratio & Proportion? Adigite cheptha. Let’s conquer Maths 35+ marks! 💪
Step 1: Introduction & NTPC Relevance
Friends, Time & Distance ante "speed tho entha dooram, entha time" – real-life physics base.
| Sub-Topic | CBT 1 Qs | CBT 2 Qs | % Weightage |
|---|---|---|---|
| Basic Speed | 1 | 1-2 | 3-6% |
| Trains | 1 | 1-2 | 3-6% |
| Boats & Streams | 0-1 | 1 | 3-5% |
| Average/Circular | 0-1 | 1 | 3-5% |
| Total | 2-4 | 3-5 | 12-14% |
Telugu: Ee topic Time & Work tho link undi – efficiency = speed. 2025 lo trains + platform, relative speed, average speed tricks common. English: Core formula = Distance = Speed × Time. Master for 100% accuracy.
Step 2: Core Concepts (Building Blocks)
| Term | Telugu Meaning | English |
|---|---|---|
| Speed (S) | Vegam (km/hr or m/s) | Distance per unit time |
| Distance (D) | Dooram | Total path |
| Time (T) | Samayam | Duration |
| Relative Speed | Oppu vegam | When moving same/opposite |
| Average Speed | Sarvasati vegam | Total D / Total T |
Telugu: 1 km/hr = 5/18 m/s. Convert chey – NTPC lo m/s lo vastundi. English: 1 km/hr = 5/18 m/s, 1 m/s = 18/5 km/hr.
Step 3: All Key Formulas (18+ with Telugu)
| # | Formula | Telugu | Example |
|---|---|---|---|
| 1 | D = S × T | Dooram = Speed × Time | 60 km/hr × 2 hrs = 120 km |
| 2 | S = D / T | Speed = Dooram / Samayam | 120 / 2 = 60 |
| 3 | T = D / S | Time = Dooram / Speed | 120 / 60 = 2 |
| 4 | Relative Speed (Same Dir) | S1 - S2 | 50 - 30 = 20 km/hr |
| 5 | Relative Speed (Opp Dir) | S1 + S2 | 50 + 30 = 80 km/hr |
| 6 | Time to meet (Opp) | D / (S1+S2) | 100 / 80 = 1.25 hrs |
| 7 | Time to cross (Same) | (L1+L2) / (S1-S2) | (200+300)/(50-30) = 25 min |
| 8 | Train crossing platform | (Train + Platform) / Speed | (200+300)/60 = 500/60 hrs |
| 9 | Average Speed | Total D / Total T | (100+100)/(2+3) = 40 km/hr |
| 10 | Average (Equal D) | 2ab/(a+b) | 2×50×60/(50+60) ≈54.55 |
| 11 | Boat Upstream | B - S | 10 - 2 = 8 km/hr |
| 12 | Boat Downstream | B + S | 10 + 2 = 12 km/hr |
| 13 | Boat Speed in still | (D+U)/2 | (12+8)/2 = 10 |
| 14 | Stream Speed | (D-U)/2 | (12-8)/2 = 2 |
| 15 | Circular Track (Same) | (L)/(S1-S2) | Lap time |
| 16 | Circular (Opp) | (L)/(S1+S2) | Faster lap |
| 17 | Time to meet first | Track / Rel Speed | 1 km / 10 = 0.1 hrs |
| 18 | Wrong direction average | (a+b)/2 if equal time | Standard |
English: Relative speed = key. Convert units always.
Step 4: Shortcuts & Hacks (NTPC Speed Boosters)
| # | Shortcut | Use |
|---|---|---|
| 1 | km/hr to m/s: ×5/18 | 36 × 5/18 = 10 m/s |
| 2 | m/s to km/hr: ×18/5 | 10 × 18/5 = 36 km/hr |
| 3 | Train time: sec = (L1+L2)/S | S in m/s |
| 4 | Average: 2ab/(a+b) | Equal distance |
| 5 | Boat: (D+U)/2 | Still water |
| 6 | Relative: Opp = +, Same = - | Direct |
| 7 | Platform = Train + Plat | Crossing time |
| 8 | Time ratio = 1/Speed | Inverse |
| 9 | Circular first meet | Track / Rel Speed |
| 10 | Wrong avg = (a+b)/2 | Equal time |
Telugu: 5/18 trick 2 secs lo. English: Memorize conversion & average formula.
Step 5: Step-by-Step Examples (6 NTPC Level)
Example 1 (Basic - CBT 1) Q: Car covers 240 km in 4 hrs. Speed? Step 1: S = 240 / 4 = 60 km/hr Telugu: Direct formula.
Example 2 (Trains Same Dir - CBT 2) Q: Train A (100m) at 54 km/hr, B (150m) at 36 km/hr same dir. Time to cross? Step 1: Convert: 54=15 m/s, 36=10 m/s Step 2: Rel Speed = 15-10 = 5 m/s Step 3: Length = 100+150 = 250 m Step 4: Time = 250 / 5 = 50 sec
Example 3 (Boats & Streams - 2025 Trend) Q: Boat downstream 30 km in 2 hrs, upstream 20 km in 2 hrs. Still water speed? Step 1: D = 30/2 = 15 km/hr, U = 20/2 = 10 km/hr Step 2: B = (15+10)/2 = 12.5 km/hr
Example 4 (Average Speed) Q: 60 km at 40 km/hr, return at 60 km/hr. Average? Step 1: Total D = 120 km Step 2: Time = 60/40 + 60/60 = 1.5 + 1 = 2.5 hrs Step 3: Avg = 120 / 2.5 = 48 km/hr Shortcut: 2×40×60/(40+60) = 48 ✓
Example 5 (Circular Track - Hard) Q: A & B run opposite on 1 km track at 10 & 8 km/hr. First meeting time? Step 1: Rel Speed = 10+8 = 18 km/hr = 5 m/s Step 2: Time = 1000 / 5 = 200 sec
Example 6 (Train + Platform + Leak - Tricky 2025) Q: Train 200m crosses platform 300m in 25 sec. Speed? If leak in engine reduces speed by 20%, new time? Step 1: Total = 500 m in 25 sec → S = 500/25 = 20 m/s = 72 km/hr Step 2: New S = 80% → 57.6 km/hr Step 3: Time = 500 / (57.6 × 5/18) = 500 / 16 = 31.25 sec
Step 6: Practice Questions (14 Graded)
Easy
- 180 km in 3 hrs. Speed?
- Speed 60 km/hr. Time for 300 km?
Medium 3. Two cars 100 km apart, speeds 40 & 60 km/hr opposite. Meet in? 4. Train 150m at 72 km/hr crosses man in 6 sec. Length? 5. Boat downstream 36 km in 3 hrs, upstream 24 km in 3 hrs. Stream speed?
Hard 6. A walks 4 km/hr, B cycles 12 km/hr same dir. A starts 1 hr early. B meets in how much time from start? 7. Train crosses pole in 10 sec, platform 400m in 30 sec. Train length? 8. Average speed: 50 km at 50 km/hr, 50 km at 100 km/hr? 9. Circular track 5 km. A=15 km/hr, B=10 km/hr opposite. Meet 3rd time after? 10. Car goes 120 km at x km/hr, returns at (x+20). Average = 60 km/hr. x? 11. Two trains 120m & 180m, speeds 60 & 48 km/hr same dir. Time to cross? 12. Boat still water 15 km/hr, stream 3 km/hr. Time to go 30 km upstream & return? 13. A runs at 6 km/hr around 400m track. Time for 1 lap? 14. Speed increases 20% every hour. Distance in 3 hrs if initial 60 km/hr?
Step 7: Answers + Explanations
- 60 km/hr
- 5 hrs
- 1 hr (100/(40+60))
- 120 m (72×5/18 ×6)
- 3 km/hr ((12-8)/2)
- 2 hrs (relative calc)
- 200 m
- 66.67 km/hr
- 1 hr (complex)
- 40 km/hr
- 30 sec
- 4.8 hrs
- 4 min
- 259.2 km
Step 8: 2025 Strategy + Common Mistakes
Strategy:
- Daily: 50 questions (RS Aggarwal Ch. 17).
- Convert Table: 18/5, 5/18 memorize.
- Mock: Testbook 2025 – Trains section.
- Link: Speed = 1/Efficiency (Part 4), % change (Part 1).
Avoid:
- Unit forget (km/hr vs m/s).
- Same dir + use cheyadam.
- Average = (a+b)/2 for distance.
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