A train, running at (3/7)th of its own speed, reached the destination in 14…

2024

A train, running at (3/7)th of its own speed, reached the destination in 14 hours. How much time could have been saved if the train had run at its own (full) speed?

  1. A.

    6

  2. B.

    8

  3. C.

    11

  4. D.

    10

Show answer & explanation

Correct answer: B

Concept

For a fixed distance, speed and time are inversely proportional: Speed × Time = Distance (constant). So if speed changes by some ratio, time changes by the reciprocal ratio.

Application

  1. The train's slower speed is (3/7) of its usual speed, so slower speed : usual speed = 3 : 7.

  2. Since time is inversely proportional to speed, time at slower speed : usual time = 7 : 3 (the ratio flips).

  3. The time at slower speed corresponds to 7 units and equals the given 14 hours, so 1 unit = 14 ÷ 7 = 2 hours.

  4. The usual (full-speed) time is 3 units = 3 × 2 = 6 hours.

  5. Time saved = time at slower speed − usual time = 14 − 6 = 8 hours.

Cross-check

At the slower speed (3/7 of usual), time taken = usual time × (7/3) = 6 × 7/3 = 14 hours — this matches the given data, confirming the usual time of 6 hours and a saving of 8 hours.

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