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If there is a policy that 1/3rd of population of a community has migrated every year from one place, to some other place, what is the leftover population of that community after the sixth year, if there is no further growth in the population during this period? 

(a) 16/243rd part of the population 

(b) 32/243rd part of the population 

(c) 32/729th part of the population 

(d) 64/729th part of the population

1 Answer

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Best answer

Correct option (d) 64/729th part of the population

Explanation:

One third of the population migrates every year. If initially the population was x, after the first year it will be x – x/3 = x (1 – 1/3) = 2x/3 

After second year, population = (2x/3) × (1 – 1/3) = (2/3)2 x

Similarly, after sixth year, population = (2/3)6 x = (64/729) x, i.e. 64/729th part of the original population. 

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