Key facts

  • The conversion 1 km/h = 5/18 m/s and 1 m/s = 18/5 km/h is the main anchor for train, platform and crossing questions.
  • For equal distances at two speeds, average speed is 2uv/(u+v), not the arithmetic mean of the two speeds.
  • In time-and-work questions, a worker completing a job in n days has a one-day rate of 1/n of the work.
  • Rajasthan's total road length up to March 2025 was 3,35,306 km, a useful one-line context for road-speed numeracy.

Key Points at a Glance

  1. 1

    Distance, speed and time questions use one identity: distance = speed x time; all units must be made consistent before substitution.

  2. 2

    The conversion 1 km/h = 5/18 m/s and 1 m/s = 18/5 km/h is the main anchor for train, platform and crossing questions.

  3. 3

    For equal distances at two speeds, average speed is 2uv/(u+v), not the arithmetic mean of the two speeds.

  4. 4

    Relative speed is the difference in the same direction and the sum in the opposite direction.

  5. 5

    In time-and-work questions, a worker completing a job in n days has a one-day rate of 1/n of the work.

  6. 6

    In pipes and cisterns, inlet rates are added and outlet rates are subtracted; a wrong sign changes the whole result.

  7. 7

    Rajasthan's total road length up to March 2025 was 3,35,306 km, a useful one-line context for road-speed numeracy.

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Core Relation in Time, Speed and Distance

Time, speed and distance questions become simple when the sentence is first converted into one relation: distance = speed x time. The same identity gives time = distance/speed and speed = distance/time. In objective questions, the stem may describe roads, trains, people, boats or travel windows, but the calculation still depends on this triangle. The first step is to identify what is asked, the second is to set the unknown, and the third is to place all values in one unit system.

Unit consistency is not optional. If distance is in metres and time is in seconds, speed must be in metres per second. If distance is in kilometres and speed is in kilometres per hour, time will come in hours. A long stem often hides this simple rule under names and context. Rajasthan's total road length up to March 2025 of 3,35,306 km is a realistic background for road-distance questions, but the equation remains the same.

Exam use: write the triangle first, convert units before calculation, and reject any answer with impossible speed or negative time.

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