Last Updated: April 2026
Time, Speed, Distance and Work is the single highest-weighted topic in IPMAT Quantitative Ability, contributing 6–9 questions every year across IPMAT Indore, IPMAT Rohtak, and JIPMAT. In IPMAT 2025 (IIM Indore), this cluster accounted for 8 questions — worth 32 marks. Mastering this chapter is non-negotiable for IPM aspirants.
Key Formulas — Time, Speed, Distance
| Concept | Formula |
|---|---|
| Basic relation | Distance = Speed × Time |
| Speed conversion | km/h × (5/18) = m/s; m/s × (18/5) = km/h |
| Average speed (same distance) | 2uv/(u+v) — NOT (u+v)/2 |
| Average speed (same time) | (u+v)/2 |
| Relative speed (same direction) | |v₁ − v₂| |
| Relative speed (opposite direction) | v₁ + v₂ |
Train Problems
When a train crosses an object, use: Time = (Length of train + Length of object) / Relative Speed
- Train crossing a pole/person: only train length counts; time = train length / speed
- Train crossing a platform: time = (train + platform length) / speed
- Two trains crossing each other: time = (sum of lengths) / (sum of speeds if opposite; difference if same direction)
Example
A 200 m train at 72 km/h crosses a 300 m platform.
Speed = 72 × (5/18) = 20 m/s
Time = (200 + 300)/20 = 25 seconds
Boats and Streams
| Term | Formula |
|---|---|
| Downstream speed | Boat speed (b) + Current speed (c) |
| Upstream speed | Boat speed (b) − Current speed (c) |
| Boat speed | (Downstream + Upstream) / 2 |
| Current speed | (Downstream − Upstream) / 2 |
| Distance upstream = Distance downstream | Time ratio = (b+c):(b−c) |
Important Time-Speed Shortcuts
Shortcut 1: Meeting Time
Two persons A (speed uA) and B (speed uB) start simultaneously from two ends of a road of length D and move towards each other:
Time to meet = D / (uA + uB)
If they move in the same direction: Time to meet = D / |uA − uB|
Shortcut 2: Late/Early Problem
If someone reaches late by L minutes at speed s₁ and early by E minutes at speed s₂, the correct time would be at a third speed. Distance formula:
D = s₁ × s₂ × (L + E) / (s₂ − s₁) × (1/60) km
Shortcut 3: Circular Track
Two persons on a circular track of length L starting from same point:
- Opposite direction: first meet after L/(u₁+u₂) time
- Same direction: first meet after L/|u₁−u₂| time
Time and Work
| Concept | Formula |
|---|---|
| Work rate | If A completes work in n days → A’s rate = 1/n per day |
| Combined rate | A and B together: 1/a + 1/b per day; total time = ab/(a+b) |
| Pipes and cisterns | Filling pipe: +1/n; Emptying pipe: −1/n; Net rate = sum |
| Men-days relation | M₁D₁H₁/W₁ = M₂D₂H₂/W₂ (when efficiency is equal) |
Key Work Problems
Example 1: A does work in 10 days, B in 15 days. Together = ab/(a+b) = 10×15/25 = 6 days
Example 2: A fills tank in 6 hours, B empties in 8 hours. Net rate = 1/6 − 1/8 = (4−3)/24 = 1/24 per hour → 24 hours to fill
Example 3 (Efficiency): 10 men complete a job in 12 days. How many men to do it in 8 days?
Men × Days = constant → M₂ = 10×12/8 = 15 men
Speed-Time-Work Integration Problems (IPMAT Favourite)
These combine speed and work: “A and B together can paint a house in 6 days. A alone takes 10 days. B’s speed is what fraction of A’s?”
- A’s rate = 1/10, combined = 1/6
- B’s rate = 1/6 − 1/10 = (5−3)/30 = 2/30 = 1/15
- B takes 15 days alone. B’s rate / A’s rate = (1/15)/(1/10) = 2:3
IPMAT Strategy for T-S-D
- Convert units first — always resolve to consistent units (km and hours, or m and seconds) before calculating
- Draw the scenario — for relative motion problems, a quick sketch prevents direction errors
- Use the LCM method for work problems — assign total work = LCM(days), find daily rates as integers (avoids fractions)
- Verify with extreme cases — if speeds are equal, relative speed should be 0 (same direction)
- Time per question: 90 seconds — IPMAT QA section averages 50 questions in 75 minutes
Practice MCQs — IPMAT T-S-D 2027
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Frequently Asked Questions (FAQ)
Why is average speed NOT the arithmetic mean of speeds?
Average speed = Total distance / Total time. When the same distance is covered at two different speeds u and v, the formula becomes 2uv/(u+v) — the harmonic mean. The arithmetic mean (u+v)/2 is only correct when the same time is spent at each speed. Confusing these two is the most common IPMAT error in TSD.
How much weightage does TSD carry in IPMAT?
In IPMAT Indore (IIM Indore), Time-Speed-Distance and Time-Work together typically account for 6–9 questions out of 50 in Quantitative Ability Section-2 (MCQ). In IPMAT Rohtak and JIPMAT, the weightage is similar. It is consistently the highest-weighted arithmetic topic.
What is the LCM method in Time and Work?
In the LCM method, you assume total work = LCM of all individual days. For example, if A takes 10 days and B takes 15 days, LCM = 30. A’s rate = 30/10 = 3 units/day; B’s rate = 30/15 = 2 units/day. Together = 5 units/day; time = 30/5 = 6 days. This avoids fractions and speeds up calculations.
How do I calculate speed in m/s from km/h?
Multiply km/h by 5/18 to get m/s. For example, 72 km/h = 72 × (5/18) = 20 m/s. To convert back from m/s to km/h, multiply by 18/5. This conversion is essential for train and running problems where lengths are in metres and speeds are given in km/h.
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