CAT Quant · Study & Practice

Trains

AreaArithmetic DifficultyEasy–Moderate CAT weightage1–2 questions (directly, plus inside broader Time-Speed-Distance sets)

Trains problems are Time-Speed-Distance (TSD) questions with one extra idea: a train has length, so the distance it must travel to "cross" something is not zero. To pass a stationary point — a pole, a man standing on a platform, a signal post — the train must move its own length, because the engine reaches the point first and the guard’s coach leaves it last. To cross a platform, a bridge or a tunnel, it must cover its own length PLUS the length of that object. When two trains cross each other, the distance covered is the SUM of their lengths, and the speed that matters is their relative speed — the sum of speeds if they move in opposite directions, the difference if they move the same way. That single relative-speed idea, paired with the constant 5/18 to switch km/h to m/s, solves almost every train question CAT or XAT throws at you. This chapter builds the three core cases in order — crossing a point, crossing a platform, two trains crossing — each with the fast multiplier method, worked examples and the traps that cost careless students a clean mark.

Topics

1 Crossing a Point 4 worked · 5 practice · 8-Q test Start → 2 Crossing a Platform 4 worked · 5 practice · 8-Q test Start → 3 Two Trains Crossing 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.

  • Crossing a POINT means crossing your own length; crossing a PLATFORM means own length + platform length. Decide which before writing an equation.
  • Memorise km/h → m/s pegs: 18=5, 36=10, 54=15, 72=20, 90=25, 108=30. Multiply any speed by 5/18 to switch.
  • Two trains: distance is always L₁ + L₂. Opposite ⇒ ADD speeds, same direction ⇒ SUBTRACT.
  • Given pole-time t₁ and platform-time t₂ at the same speed: platform length = speed × (t₂ − t₁), and speed = length ÷ t₁.
  • Two crossing times (opposite t_o, same t_s) for the same pair: sum of speeds = (L₁+L₂)/t_o, difference = (L₁+L₂)/t_s; then split.
  • A man/pole is a point (length 0). A bridge/tunnel/platform is a length — never treat them the same way.

⚠️ Common mistakes & traps

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

  • Forgetting to add the platform length — using only the train’s length to cross a platform.
  • Mixing units: dividing a length in metres by a speed in km/h without the 5/18 conversion.
  • Adding speeds for same-direction overtaking (should subtract) or subtracting for opposite directions (should add).
  • Using only ONE train’s length when two trains cross — the distance is the SUM of both lengths.
  • Treating a moving man as a point but forgetting his speed adds to or subtracts from the train’s relative speed.

📈 CAT exam insight & PYQ analysis

In CAT and XAT, pure "trains" questions are now rare as standalone items; they surface mostly as one part of a Time-Speed-Distance problem or a logic-flavoured arithmetic set. When they do appear, the favourite patterns are: the pole-time-plus-platform-time pair that asks for the train’s length or speed, and the two-trains-crossing twist that supplies both same-direction and opposite-direction times. Difficulty is Easy–Moderate, but careless unit conversion (km/h vs m/s) and direction errors (add vs subtract) are the usual reasons a sure mark is dropped. Prioritise speed and clean 5/18 arithmetic over memorising obscure formulas.

🎴 Flashcards — instant recall

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

Distance to cross a pole/point?Tap to reveal
The train’s own length
Distance to cross a platform?Tap to reveal
Train length + platform length
km/h to m/s — multiply by?Tap to reveal
5/18
m/s to km/h — multiply by?Tap to reveal
18/5
72 km/h in m/s?Tap to reveal
20 m/s
Two trains, opposite directions — relative speed?Tap to reveal
Sum of the two speeds
Two trains, same direction — relative speed?Tap to reveal
Faster − slower
Distance when two trains cross?Tap to reveal
L₁ + L₂ (sum of lengths)
Time to cross a platform?Tap to reveal
(L_train + L_platform) ÷ speed
Platform length from pole-time t₁ and platform-time t₂?Tap to reveal
speed × (t₂ − t₁)
90 km/h in m/s?Tap to reveal
25 m/s
Train and a man moving the same way at equal speed cross in?Tap to reveal
Never (relative speed 0)

📌 Quick revision

A train must cover its OWN length to cross a point (pole/man/signal): time = length ÷ speed. To cross a platform/bridge/tunnel, add the platform length: time = (train + platform) ÷ speed. When two trains cross, the distance is the SUM of their lengths and the speed is relative — ADD speeds for opposite directions, SUBTRACT for the same direction. Always convert km/h to m/s with 5/18 before dividing, and keep the train’s length fixed across paired pole/platform equations. The classic traps: skipping the platform length, mixing units, and reversing the add/subtract rule for direction.

Chapter test

📝 Trains — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
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🏆 Vidaara CAT success checklist

You have truly mastered Trains 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 (3 topics)3/3
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall12 cards