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On a circular track, a man covers half distance at 4 km/hr, next half of remaining half at 5 km/hr, next half of remaining half at 6 km/hr and so on till his speed reaches 10 km/hr after which he covers remaining distance at 10 km/hr to complete one round. Then find his average speed?

On a circular track, a man covers half distance at 4 km/hr, next half of remaining half at 5 km/hr, next half of remaining half at 6 km/hr and so on till his speed reaches 10 km/hr after which he covers remaining distance at 10 km/hr to complete one round. Then find his average speed? Correct Answer 695/4032

Let total distance in one round is d.

Average speed = total distance/total time

Average speed = d/(d/2/5 + d/4/6 + d/8/7 + d/16/8 + d/32/9 + d/64/10)

Average speed = 1/(1/10 + 1/24 + 1/56 + 1/128 + 1/288 + 1/640)

∴ Average speed = 695/4032

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