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If a girl cycles at 10 kmph, then she arrives at a certain place at 1 p.m. If she cycles at 15 kmph, she will arrive at the same place at 11 a.m. At what speed must she cycle to get there at noon?

Correct Answer: 12 kmph

Explanation:

The distance is constant in this case.


Let the time taken for travel with a speed of 10 kmph be 't'.


Now the speed of 15 kmph is 3/2 times the speed of 10 kmph.


Therefore, time taken with the speed of 15 kmph will be 2t/3 (speed is inversely proportional to time)


Extra time taken = t - 2t/3 = t/3


=> 1pm - 11am = 2hrs


=> t/3 = 2h


=> t = 6 hrs.


Now, Distance = speed x time = 10 x 6 = 60 kms


Time he takes to reach at noon = 6 - 1 = 5 hrs


Now, Speed = 60/5 = 12 kmph.


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