Multiple choice

If Anuj walks at the rate of 5 kmph, he misses the train by 6 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 6 minutes before the arrival of the train. Find the distance covered by him to reach the station.

  1. 8 km

  2. 5 km

  3. 6 km

  4. 7 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be D. Time taken at 5 kmph is D/5, and at 6 kmph is D/6. The difference in time is 12 minutes (6 minutes late + 6 minutes early = 12 minutes = 0.2 hours). D/5 - D/6 = 0.2. Solving gives D/30 = 0.2, so D = 6 km.

AI explanation

Let the exact time to reach the station be t hours. Since distance equals speed multiplied by time, the distance is 5 multiplied by (t + 0.1) and also 6 multiplied by (t - 0.1). Equating the two gives 5t + 0.5 equals 6t - 0.6, so t = 1.1 hours. Substituting this back gives the distance as 6 multiplied by (1.1 - 0.1), which equals 6 km.

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