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Question

A student walks to school at the rate of 7.5 km/hr and reaches 10 minutes late. If he walks at the speed of 10 km/hr he is 10 minutes early. What is the distance to the school in km?
  1. 10

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Solution

The correct option is A 10
Let the distance to the school be 1 km, then the time taken to cover 1 km at the rate of 7.5 km/hr is DistanceSpeed=1152 hr =215×60 min =8 min

Time taken to cover 1 km at the rate of 10 km/hr =DistanceSpeed=110 hr=110×60 min=6 min

Difference in time taken = ( 8 - 6 ) = 2 min.

When the difference in time is 2 min, the distance is 1 km.

The student reaches 10 min late with 7.5 km/hr and 10 min early with 10 km/hr, so the time difference is 20 min.

For the time difference of 20 min, the distance is 202=10 km

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