Time Speed Distance for IPMAT 2026: Master Arithmetic in 30 Days
Time Speed Distance (TSD) is one of the highest-scoring topics in IPMAT Quantitative Ability. Every year, 2–4 questions from TSD appear in IPMAT Indore and Rohtak, making it a non-negotiable topic in your preparation. The good news: TSD is systematic, formula-based, and becomes highly predictable once you understand the 6 core pattern types.
This guide covers all key IPMAT TSD formulas, 7 solved examples, 30 practice problems with solutions, and common traps that cost students marks.
Core TSD Formulas for IPMAT
| Formula | Expression | When to Use |
|---|---|---|
| Basic Speed | Speed = Distance ÷ Time | Any direct TSD question |
| Average Speed (same distance) | 2ab/(a+b) | To-and-fro journeys at different speeds |
| Relative Speed (opposite) | v₁ + v₂ | Two objects moving towards each other |
| Relative Speed (same direction) | v₁ − v₂ | One object chasing another |
| Train crossing a pole | Speed = Length ÷ Time | Train vs stationary point |
| Train crossing a platform | Speed = (Train length + Platform length) ÷ Time | Train vs extended object |
| Boats upstream speed | u − c (u = boat speed, c = current) | Upstream boat problems |
| Boats downstream speed | u + c | Downstream boat problems |
| Speed conversion | km/h × 5/18 = m/s | Unit conversion in any TSD |
TSD Question Types in IPMAT: Frequency Analysis
| Question Type | IPMAT Frequency | Difficulty | Time to Solve |
|---|---|---|---|
| Average speed (same/different distance) | Very High | Easy | 45 sec |
| Train problems (crossing objects) | High | Easy-Medium | 60 sec |
| Chase problems (thief-police type) | Medium | Medium | 75 sec |
| Boat and stream | Medium | Medium | 75 sec |
| Meeting point problems | Medium | Medium | 60 sec |
| Circular track problems | Low | Hard | 90+ sec |
7 Solved TSD Examples for IPMAT
Problem 1: Average Speed
Q: A car travels 120 km at 60 km/h and another 120 km at 40 km/h. Find the average speed.
Solution: Same distance, different speeds → Use harmonic mean: 2ab/(a+b) = 2 × 60 × 40/(60+40) = 4800/100 = 48 km/h
Problem 2: Average Speed (Different Distances)
Q: A car travels at 60 km/h for 2 hours and 80 km/h for 3 hours. Find average speed.
Solution: Total distance = 60×2 + 80×3 = 120 + 240 = 360 km. Total time = 5 hrs. Avg speed = 360/5 = 72 km/h
Problem 3: Train Crossing a Platform
Q: A 300m long train passes a 200m platform in 25 seconds. Find the speed of the train.
Solution: Speed = (300 + 200)/25 = 500/25 = 20 m/s = 20 × 18/5 = 72 km/h
Problem 4: Two Trains Crossing Each Other
Q: Two trains 150m and 250m long run towards each other at 40 km/h and 50 km/h. Time to cross?
Solution: Total length = 400m. Relative speed = 90 km/h = 25 m/s. Time = 400/25 = 16 seconds
Problem 5: Chase Problem
Q: A thief runs at 10 km/h. Police start chase after 3 minutes at 14 km/h. When is thief caught?
Solution: Head start = 10 × 3/60 = 0.5 km. Relative speed = 4 km/h. Time = 0.5/4 hr = 7.5 minutes
Problem 6: Boats and Streams
Q: A boat goes 30 km downstream in 2 hours and 20 km upstream in 4 hours. Find the speed of the current.
Solution: Downstream speed = 15 km/h. Upstream speed = 5 km/h. Current = (15-5)/2 = 5 km/h
Problem 7: Meeting Point
Q: A and B are 450 km apart. They start simultaneously towards each other at 80 and 100 km/h. When do they meet?
Solution: Combined speed = 180 km/h. Time = 450/180 = 2.5 hours
30 IPMAT TSD Practice Problems (Categorized)
Set A: Average Speed (10 Problems)
- A man walks at 4 km/h to office and returns at 6 km/h. Average speed? Answer: 4.8 km/h
- A bus covers first 100 km at 50 km/h and next 150 km at 75 km/h. Average speed? Answer: 62.5 km/h
- A cyclist covers equal distances at 10, 15, and 20 km/h. Average speed? Answer: ~13.85 km/h
- Two cars travel 200 km each — Car A at 80 km/h, Car B at 100 km/h. Average speed of journey if same car? Depends on context
- A student walks to school at 3 km/h. If she ran at 9 km/h, she’d reach 20 min early. Find distance. Answer: 1.5 km
- A car covers 1/3 of journey at 30 km/h, 1/3 at 60 km/h, remaining at 90 km/h. Average speed? Answer: 49.1 km/h
- A train travels 240 km at 80 km/h then 120 km at 60 km/h. Find total time. Answer: 5 hours
- If speed is increased by 25%, time is reduced by how much percent? Answer: 20%
- A travels from P to Q at 60 km/h and returns at 40 km/h. Average speed? Answer: 48 km/h
- Ramesh covers half the journey at 20 km/h and half at 30 km/h. Average speed for entire journey? Answer: 24 km/h
Set B: Train Problems (10 Problems)
- Train 200m long passes a tree in 10 sec. Speed in km/h? Answer: 72 km/h
- Train 500m long runs at 36 km/h. Time to cross a 1000m bridge? Answer: 150 sec
- Two trains of 100m and 200m run in same direction at 72 and 36 km/h. Time to cross? Answer: 30 sec
- A person on platform sees a 500m train pass in 50 sec. Speed? Answer: 36 km/h
- Trains A (300m, 72 km/h) and B (200m, 36 km/h) run opposite. Time to cross? Answer: 20 sec
- Train doubles its speed and saves 2 hours on 240 km journey. Original speed? Answer: 60 km/h
- A 300m train crosses a man in 30 sec and a platform in 60 sec. Platform length? Answer: 300m
- Two trains leave simultaneously from A and B (400 km apart) at 60 and 40 km/h. When do they meet? Answer: 4 hours
- A train running at 54 km/h crosses a pole in 10 sec. Length? Answer: 150m
- A train crosses a 400m bridge in 30 sec at 72 km/h. Train length? Answer: 200m
Set C: Boats, Chase & Meeting Problems (10 Problems)
- Boat speed 12 km/h, current 4 km/h. Time to go 32 km downstream? Answer: 2 hours
- Boat covers 24 km upstream in 6 hrs, downstream in 3 hrs. Speed of current? Answer: 2 km/h
- Thief at 8 km/h, police at 12 km/h with 2 km head start. Time to catch? Answer: 30 min
- A and B run a 1000m race. A wins by 100m. If both start together, by how many seconds? Answer: Depends on A’s speed
- Ram and Shyam start from same point at 6 km/h and 10 km/h. After how long is B 2 km ahead? Answer: 30 min
- Two people walk towards each other from 10 km apart at 3 and 2 km/h. When do they meet? Answer: 2 hrs
- A starts 3 hours before B from same point. B walks twice A’s speed. When does B overtake A? Answer: 3 hours after B starts
- P and Q start at opposite ends of 5 km track. Speeds 2 and 3 km/h. Meeting point from P? Answer: 2 km
- Downstream speed 15 km/h, upstream 9 km/h. Find still water speed. Answer: 12 km/h
- Boat rows 18 km downstream in 2 hrs and 12 km upstream in 3 hrs. Current speed? Answer: 2 km/h
Practice Quiz: Time Speed Distance IPMAT
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Frequently Asked Questions: TSD in IPMAT
How many TSD questions appear in IPMAT Indore?
IPMAT Indore typically has 2–4 Time Speed Distance questions across its MCQ and Short Answer sections. These questions test average speed, train crossing, and boat-stream problems. In IPMAT Rohtak, TSD appears in the Quantitative Ability section with 1–3 questions. Since IPMAT Indore has 40 MCQ + 20 SA questions, TSD constitutes about 3–5% of the paper.
What is the formula for average speed in IPMAT TSD problems?
For equal distances: Average speed = 2ab/(a+b) where a and b are the two speeds. Example: travel to office at 4 km/h, return at 6 km/h → avg speed = 2×4×6/(4+6) = 48/10 = 4.8 km/h. For unequal distances, use: total distance / total time. Never average the speeds directly.
How do I convert km/h to m/s for IPMAT train problems?
To convert km/h to m/s, multiply by 5/18. Example: 72 km/h × 5/18 = 20 m/s. To convert m/s to km/h, multiply by 18/5. Example: 20 m/s × 18/5 = 72 km/h. This conversion is critical in train crossing problems where train length is given in meters and speed in km/h.
What is the difficulty level of TSD in IPMAT compared to CAT?
TSD in IPMAT is easier than in CAT but harder than in SSC. IPMAT TSD focuses on direct formula application and one-step reasoning. CAT TSD often involves multi-step problems with circular tracks and complex relative motion. For IPMAT, mastering 6 formula types and 20–25 practice problems is sufficient. For CAT, you’d need 100+ varied problems.
Related Posts: IPMAT Indore 2026 Complete Guide