Multiple choice

Sumit travels by metro train. He goes at a speed of 15 km/hr and reaches the station 3 minutes late. He increases his speed to 20 km/hr and reaches 2 minutes earlier. What is the distance between his home and the metro station?

  1. 5 km

  2. 6 km

  3. 10 km

  4. 5.25 km

  5. 15 km
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A Correct answer
Explanation

Let distance be D. Time at 15 km/hr is D/15, time at 20 km/hr is D/20. The difference in time is 3 minutes late + 2 minutes early = 5 minutes = 5/60 hours. So, D/15 - D/20 = 5/60. (4D - 3D)/60 = 5/60, which gives D = 5 km.

AI explanation

Using the constant distance formula, the distance equals the product of the two speeds and the total time difference, divided by the difference of their squares. Converting the total time difference of 5 minutes into hours gives 5/60, or 1/12 hours. The calculation becomes (15 multiplied by 20 multiplied by 1/12) divided by (400 minus 225), resulting in 25 divided by 5, which equals 5 km.

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