CAT Quant · Study & Practice

Time, Speed & Distance

AreaArithmetic DifficultyModerate CAT weightage2–4 questions (directly + inside Time-Work, Boats-Streams, Clocks and DI)

Time, Speed and Distance is the workhorse of CAT Arithmetic. Every question in this chapter rests on one relationship — distance = speed × time — yet examiners stretch it into dozens of disguises: a train crossing a pole, two cars closing a gap, a runner giving a head start, a swimmer fighting a current. What makes the topic high-yield is that the same logic powers Boats & Streams, Races, Clocks, and several Data Interpretation sets, so fluency here pays off far beyond a single question. CAT rarely asks a plain "find the speed"; it hides the formula inside ratios (when distance is fixed, speed and time are inversely proportional), inside relative motion (add speeds when objects approach, subtract when they chase), and inside weighted averages (average speed is total distance over total time, never the simple mean). This chapter builds the chain from the ground up: converting km/h to m/s with the 5/18 factor, computing true average speed including the 2xy/(x+y) shortcut for equal distances, handling relative speed in both directions, and decoding races with head starts and beats — each with worked examples, the fastest method, and the traps that quietly cost marks.

Topics

1 Speed Basics 4 worked · 5 practice · 8-Q test Start → 2 Average Speed 4 worked · 5 practice · 8-Q test Start → 3 Relative Speed 4 worked · 5 practice · 8-Q test Start → 4 Pursuit & Races 4 worked · 5 practice · 8-Q test Start →

⚡ CAT shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

  • km/h → m/s: multiply by 5/18; m/s → km/h: multiply by 18/5. Memorise 36→10, 54→15, 72→20, 90→25.
  • Fixed distance ⇒ speed and time are inverse: speed ×k ⇒ time ÷k. Use ratios, skip the arithmetic.
  • Equal distances at speeds x and y ⇒ average = 2xy/(x+y); never the simple mean. Three legs ⇒ 3xyz/(xy+yz+zx).
  • Equal TIMES at two speeds ⇒ average is the simple mean (x+y)/2. Equal distances ⇒ harmonic mean.
  • Two bodies: opposite directions add speeds, same direction subtract. Meeting/catching time = gap ÷ relative speed.
  • "A beats B by d m in an L m race" ⇒ speed ratio = L : (L−d), applied to whatever distance each actually runs.

⚠️ Common mistakes & traps

CAT is designed so that careless errors here cost you marks. Internalise each trap before the exam.

  • Averaging two speeds directly (40 and 60 give 48, not 50, when distances are equal).
  • Forgetting to convert km/h to m/s (×5/18) before using metres and seconds in train problems.
  • Adding lengths wrong: crossing a pole uses only the train length; crossing a platform/train adds both lengths.
  • Using sum of speeds for same-direction motion (overtaking) or difference for opposite-direction (approaching).
  • Misreading a "beat": "beats by 20 m" is a distance gap at the finish; "beats by 5 s" is a time gap for the same distance.

📈 CAT exam insight & PYQ analysis

In recent CATs, Time-Speed-Distance appears in 2–4 questions, frequently fused with Time & Work, Boats & Streams, or circular-track meetings rather than as plain formula plug-ins. Recurring patterns: average speed using 2xy/(x+y), trains crossing platforms/each other via relative speed, a person reaching late/early at two different speeds (the "distance from late–early gap" template), and races framed as speed ratios. XAT and IIFT lean harder on circular tracks and multi-leg journeys. Difficulty is Moderate, but the harder set-ups reward students who model with ratios and convenient assumed distances instead of grinding raw numbers — speed of setup decides the percentile.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

km/h to m/s conversion factor?Tap to reveal
Multiply by 5/18
m/s to km/h conversion factor?Tap to reveal
Multiply by 18/5
72 km/h in m/s?Tap to reveal
20 m/s
Average speed for equal distances at x and y?Tap to reveal
2xy/(x+y)
When does simple mean (x+y)/2 give average speed?Tap to reveal
Equal times spent at each speed
Relative speed, opposite directions?Tap to reveal
Sum of the two speeds
Relative speed, same direction?Tap to reveal
Difference of the two speeds
Distance to cross a platform of length p (train length L)?Tap to reveal
L + p
Fixed distance: speed up by 25% ⇒ time?Tap to reveal
Falls to 4/5 (down 20%)
"A beats B by 20 m in 100 m" ⇒ speed ratio?Tap to reveal
100 : 80 = 5 : 4
Time for faster to lap slower on a track?Tap to reveal
Track length ÷ (difference of speeds)
Average speed for three equal legs x, y, z?Tap to reveal
3xyz/(xy+yz+zx)

📌 Quick revision

Distance = speed × time underpins everything. Convert units with 5/18 (km/h→m/s) and 18/5 (m/s→km/h). For a fixed distance, speed and time are inversely proportional — use ratios. Average speed is total distance ÷ total time: for equal distances apply 2xy/(x+y), and only use the simple mean for equal times. Relative speed adds for opposite directions and subtracts for the same direction; meeting or catching time = gap ÷ relative speed, and crossing a platform adds both lengths. In races, turn each "beat" into a speed ratio L:(L−d) and apply it to the leg each runner actually runs. Watch the traps: never average speeds directly, always match units, and read whether a beat is a distance or a time.

Chapter test

📝 Time, Speed & Distance — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
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🏆 Vidaara CAT success checklist

You have truly mastered Time, Speed & Distance when you can tick every box below.

  • Recall every formula in this chapter without looking them up
  • Solve each topic’s practice set with at least 80% accuracy
  • Use the chapter shortcuts to cut your solving time in half
  • Spot and avoid every common trap listed above
  • Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (4 topics)4/4
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall12 cards