Infosys Company Logical Reasoning General Mental Ability

In India, water lillies grow extremely rapidly in the ponds. If the growth enlarged so much that each day it covered a surface double that which it filled the day before, so that at the end of the 20th day if entirely covered the pond, in which it grew, how long would it take water lillies of the same size at the outset and at the same rate of growth to cover the same pond?

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A thief is capable of running 20kms a day. A policeman who is to catch the thief can run 1km on the 1st day, 2kms on the 2nd day and so on. Then how long will it take the policeman to catch the thief?