Quantitative aptitude · lesson 21 of 30 · free

Trains, boats and streams — Quantitative aptitude for kids

To pass a pole, a train covers its own length; to cross a platform, its length plus the platform. Two trains running towards each other add their speeds. A boat goes faster downstream (boat + stream) and slower upstream (boat − stream).

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The method

Length and relative speed — “a train must cover its own length (plus a platform); a river adds to or takes from a boat’s speed”

  1. Change km/h to m/s (× 5/18) when lengths are in metres and time in seconds.
  2. Pole: time = train length ÷ speed. Platform: (train + platform) ÷ speed.
  3. Towards each other: add the speeds; same direction: take them away. Cover both lengths.
  4. Downstream = boat + stream; upstream = boat − stream. Boat = (down + up) ÷ 2; stream = (down − up) ÷ 2.

Use it for: Train and boat questions in aptitude, scholarship and later competitive exams; relative speed in physics.

Worked example: A train 150 m long runs at 54 km/h. How many seconds does it take to cross a platform 300 m long? → 30

  1. 54 × 5/18 = 15 m/s.
  2. (150 + 300) ÷ 15 = 30 seconds.

Check: 15 m/s × 30 s = 450 m = 150 + 300 ✓

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