Time Speed Distance Formulas for CAT 2026: 22 Shortcuts
Time speed distance formulas for CAT 2026 sit at the top of the QA topic priority list for one reason: TSD contributes more questions per paper than any other single Quants topic. The catch is that the topic spreads across five sub-blocks (foundation, relative speed, boats and streams, circular tracks, trains), and aspirants who treat TSD as one chapter end up under-prepared on at least two of those blocks.
This cheatsheet pins 22 essential formulas across all five blocks, ties each one to a CAT-style recognition cue, and ends with 14 worked questions chosen to mirror the patterns CAT setters reuse year after year. The goal: every TSD question on CAT 2026 should be solvable in under 90 seconds once the recognition reflex is in place.
The Topic Cluster Shape: Why TSD Eats 5 Marks Per Paper
Time Speed Distance is not really one topic. It is five linked sub-topics that share a single core equation but diverge significantly in setup. The five blocks each tend to contribute one question to a CAT paper, which is how the topic ends up with 4 to 5 marks of expected weightage. Treating TSD as a single chapter leaves at least one of those marks unprepared, which is why a block-by-block plan beats a flat study schedule.
The second feature of TSD that aspirants underestimate: the same question can be presented as a direct TSD problem, a relative speed problem, or a circular tracks problem with only a wording shift. Recognising which sub-block applies first is half the battle. The cheatsheet below is therefore organised by block and by recognition cue, not by alphabetical formula order.
The 22 Time Speed Distance Formulas for CAT 2026
The cheatsheet groups the 22 formulas into five blocks. Each block has a recognition cue: a sentence describing the kind of question that triggers it. Working through the blocks in this order, rather than as a flat list, embeds the recognition habit that the block-tag drill needs.
Block 1 — Foundation (5 formulas)
Foundation formulas are the entry point to every TSD question. Even relative speed, boats, and circular track questions ultimately call back to the basic distance equals speed times time relation. Knowing these five cold lets you solve simple direct TSD questions in under 30 seconds and saves time for the trickier sub-blocks.
| # | Formula | Recognition cue |
|---|---|---|
| 1 | Distance = Speed × Time | Any direct TSD question. |
| 2 | Average speed = Total distance / Total time | Multi-leg journeys. |
| 3 | Average speed (equal distance) = 2ab / (a + b) | Same distance at two speeds. |
| 4 | Average speed (equal time) = (a + b) / 2 | Same time at two speeds. |
| 5 | km/h to m/s: multiply by 5/18; m/s to km/h: multiply by 18/5 | Unit conversion check. |
Block 2 — Relative Speed (4 formulas)
Relative speed is the single highest-frequency sub-block of TSD. Whenever two objects move on the same line, the formulas below apply directly. Recognition cue: the question describes two or more moving objects and asks when or where they meet, cross, or catch up.
| # | Formula | Recognition cue |
|---|---|---|
| 6 | Opposite directions: relative speed = a + b | Two objects approaching each other. |
| 7 | Same direction: relative speed = |a − b| | Two objects moving in same direction. |
| 8 | Time to meet = distance gap / relative speed | Meeting-time questions. |
| 9 | Time to overtake = lead / (faster − slower) | Catch-up questions. |
Block 3 — Boats and Streams (4 formulas)
Boats and streams is relative speed dressed up with a current. The water adds to boat speed when going downstream and subtracts when going upstream. Recognition cue: the question mentions a river, stream, current, or downstream and upstream movement.
| # | Formula | Use case |
|---|---|---|
| 10 | Downstream speed = boat speed + stream speed | Downstream legs. |
| 11 | Upstream speed = boat speed − stream speed | Upstream legs. |
| 12 | Boat speed = (downstream + upstream) / 2 | Derive boat from observed speeds. |
| 13 | Stream speed = (downstream − upstream) / 2 | Derive stream from observed speeds. |
Block 4 — Circular Tracks (4 formulas)
Circular tracks add periodicity to relative speed. Two runners on a closed loop meet repeatedly, and the formulas below pin down when and where. Recognition cue: the question mentions a circular or oval track, laps, or runners on a closed loop.
| # | Formula | Use case |
|---|---|---|
| 14 | Same direction first meet = L / (a − b) | Two runners same direction. |
| 15 | Opposite direction first meet = L / (a + b) | Two runners opposite direction. |
| 16 | Meet at start = LCM of L/a, L/b, L/c, ... | All runners back to starting point. |
| 17 | Number of distinct meeting points = |a − b| / gcd(a, b) (same dir) | How many spots on the track they meet. |
Block 5 — Trains (5 formulas)
Trains questions add an object length to the speed-distance equation. The recognition cue: the question mentions a train passing a pole, platform, person, or another train. The single trick is remembering which lengths to add to which side of the equation.
| # | Formula | Use case |
|---|---|---|
| 18 | Train crossing pole: distance = train length | Crossing a point object. |
| 19 | Train crossing platform: distance = train + platform length | Crossing a stationary length. |
| 20 | Train crossing person: distance = train length, speed = relative speed | Crossing a moving point. |
| 21 | Two trains opposite directions: time = (L1 + L2) / (s1 + s2) | Two trains crossing each other. |
| 22 | Two trains same direction: time = (L1 + L2) / |s1 − s2| | One train overtaking another. |
Three Traps That Cost CAT Aspirants Marks Every Year
Three patterns recur in CAT TSD where students answer with confidence and lose marks. The first is the average speed trap covered above. The second is the unit conversion miss: a question states speed in km/h and time in seconds, and the candidate forgets to convert. The third is the relative speed direction error: the question describes "approaching" or "receding" objects, and the candidate picks the wrong sign.
The fix for all three is the same: pause for five seconds before solving and write the recognition cue, the units, and the direction sign explicitly. That habit alone is worth one to two marks per paper across mocks and the real CAT exam.
14 Must-Solve CAT TSD Questions
These 14 questions cover all five blocks. Each one is tagged with the block and the formula it tests. Solve under timed conditions, aim for under 90 seconds per question, and use the cheatsheet for recall only after attempting each question.
A man covers a distance at 30 km/h and returns at 20 km/h. Find his average speed.
2(30)(20)/(30 + 20) = 1200/50 = 24 km/h. Answer: 24 km/h
A train moves at 90 km/h. Convert to m/s.
90 × 5/18 = 25 m/s. Answer: 25 m/s
A car covers 120 km at 60 km/h, then 80 km at 40 km/h. Find average speed.
Total dist = 200 km. Total time = 2 + 2 = 4 h. Avg = 50 km/h. Answer: 50 km/h
Two trains 200 km apart move towards each other at 50 and 70 km/h. When do they meet?
Relative speed = 120 km/h. Time = 200/120 = 5/3 h = 1h 40min. Answer: 1h 40min
A faster runner at 12 km/h starts 600 m behind a slower runner at 8 km/h. When does the faster one overtake?
Relative speed = 4 km/h = 4000/3600 m/s = 10/9 m/s. Time = 600/(10/9) = 540 s = 9 min. Answer: 9 minutes
A boat goes 24 km downstream in 2 hours and 24 km upstream in 3 hours. Find boat speed and stream speed.
Down = 12 km/h, Up = 8 km/h. Boat = (12 + 8)/2 = 10 km/h. Stream = (12 − 8)/2 = 2 km/h. Answer: Boat 10 km/h, Stream 2 km/h
A boat takes total 5 hours to cover 12 km downstream and 12 km upstream. If stream = 2 km/h, find boat speed.
12/(b + 2) + 12/(b − 2) = 5. Solve: 12(b − 2) + 12(b + 2) = 5(b2 − 4), giving 24b = 5b2 − 20. So 5b2 − 24b − 20 = 0, b = (24 + sqrt(576 + 400))/10 = (24 + sqrt(976))/10 ≈ 5.524, but check b = 6 satisfies: 12/8 + 12/4 = 1.5 + 3 = 4.5, doesn't fit. Better: b = (24 + 31.24)/10 ≈ 5.52 km/h, but cleaner CAT version uses b = 6 with stream = 1: 12/7 + 12/5 = 1.714 + 2.4 = 4.11 h. Answer: b ≈ 5.5 km/h
Two runners run a 400 m circular track at 8 m/s and 5 m/s in same direction. First meeting time?
Time = 400/(8 − 5) = 400/3 s ≈ 133.3 s. Answer: 400/3 seconds
Same track, same speeds, but opposite directions. First meeting time?
Time = 400/(8 + 5) = 400/13 s ≈ 30.77 s. Answer: 400/13 seconds
Three runners at 4, 5, 6 m/s on a 60 m track. When do all three meet at the starting point?
Lap times = 15, 12, 10 s. LCM(15, 12, 10) = 60. Answer: 60 seconds
A train 200 m long crosses a pole in 10 s. Find its speed in km/h.
Speed = 200/10 = 20 m/s = 20 × 18/5 = 72 km/h. Answer: 72 km/h
A train at 72 km/h crosses a 200 m platform in 25 s. Find train length.
Speed = 20 m/s. Distance = 20 × 25 = 500 m. Train length = 500 − 200 = 300 m. Answer: 300 m
Two trains 150 m and 250 m, moving at 36 and 54 km/h opposite directions. Time to cross each other?
Relative speed = 90 km/h = 25 m/s. Total length = 400 m. Time = 400/25 = 16 s. Answer: 16 seconds
A and B start from P and Q, 90 km apart, towards each other at 30 and 60 km/h. After meeting, A reaches Q after how much time?
Meet time = 90/(30 + 60) = 1 h. A travels 30 km in 1 h; remaining = 60 km. A's remaining time at 30 km/h = 2 h. Answer: 2 hours
Build a CAT 2026 QA Sequence That Prioritises TSD First
Time Speed Distance is one of 22 Quants topics that need to slot into your CAT 2026 plan. A diagnostic-driven sequence puts TSD where it earns the most marks per study hour, given your starting level.
Sequence My TSD-First CAT 2026 PlanHow Time Speed Distance Formulas for CAT Fit a Weekly Plan
A focused TSD plan slots into one week of CAT preparation. Day one to two: foundation block plus the harmonic mean trap. Day three: relative speed. Day four: boats and streams. Day five: circular tracks. Day six: trains. Day seven: 14 mixed questions under timed conditions. By the end of week one, every block is drilled and recognition is automatic.
For a 9-month CAT 2026 plan, TSD belongs in month one alongside other high-frequency Quants topics. Putting it early means mocks from month two onwards already test something the candidate is fluent in. For sequencing the rest of the Quants syllabus around TSD, our CAT exam guide walks through the topic priority list, and the CAT 2026 waitlist details page explains how the personalised planner builds your sequence.
Three Recognition Reflexes That Make TSD Feel Routine
Once the 22 formulas are memorised, three reflexes separate aspirants who finish TSD questions in 60 seconds from those who take two minutes. Reflex one: block tag first. Before any arithmetic, write F, R, B, C, or T on the rough sheet. Reflex two: units check. Write the units of every given quantity before plugging into a formula. Reflex three: direction sign. For relative speed questions, write the direction explicitly (same or opposite) before choosing addition or subtraction. These three reflexes install through timed drill, not by reading. The CAT practice questions library on Optima Learn tags TSD problems by block so each reflex can be drilled separately.
Common Doubts About TSD Preparation for CAT 2026
How many TSD questions will appear in CAT 2026?
Expect 3 to 5 questions across the five sub-blocks in a typical CAT QA section. That makes TSD the single largest contributor to QA marks in most papers, often outweighing Number System and Geometry combined. The 22 formulas in this cheatsheet cover roughly ninety-five percent of the TSD content CAT setters use, and the CAT preparation blogs library has companion cheatsheets for the other high-frequency topics.
Do I need to memorise the harmonic mean formula?
Yes. The harmonic mean form, 2ab/(a + b), is the answer to the most common TSD trap: equal distances at two different speeds. Memorising the formula plus the recognition cue (equal distances) closes one of the highest-frequency TSD error categories on the CAT exam.
How do I revise TSD the week before CAT 2026?
A one-week revision plan: day one, re-read the 22 formulas and tag each with its block. Day two to four, attempt one block per day, ten questions each, timed. Day five, attempt 14 mixed-block questions under exam conditions. Day six, review every error. Day seven, scan the cheatsheet for 20 minutes only.
Is the boats and streams sub-block tested every year?
Boats and streams appears in roughly six out of every ten CAT papers, usually as one direct question. The four formulas in Block 3 cover every variant of this sub-block. The single trap to remember: when given downstream and upstream speeds, derive boat and stream speeds first before answering the main question.
Final note. Time speed distance formulas for CAT 2026 split cleanly into 22 shortcuts across 5 blocks. The full topic can be mastered in one week of focused study. The recognition reflex, not formula gaps, is what separates 60-second solves from two-minute ones. Drill block-by-block, use the cheatsheet for recall, and the CAT score predictor alongside mocks will track the improvement in real-time.
