If there is a policy that 1/3rd of population of a community has migrated every year from one place, to some o

Question

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?

Accepted Answer

If 1/3rd of the population migrates every year, then the remaining population each year is 1 - 1/3 = 2/3rd of the population from the previous year.

Let the initial population be P.
After 1st year: P * (2/3)
After 2nd year: P * (2/3) * (2/3) = P * (2/3)^2
After 3rd year: P * (2/3)^3
...
After 6th year: P * (2/3)^6

Now, calculate (2/3)^6:
Numerator: 2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64
Denominator: 3^6 = 3 * 3 * 3 * 3 * 3 * 3 = 729

So, the leftover population is 64/729th part of the original population.

Analyzing the options:
A) 16/243rd part of the population (Incorrect. This would be (2/3)^5 / 2 or (2/3)^4 * (1/3) * 2 or similar incorrect calculation)
B) 32/243rd part of the population (Incorrect. This is (2/3)^5)
C) 32/729th part of the population (Incorrect. This is (2^5)/(3^6), which is 32/729)
D) 64/729th part of the population (Correct. This is (2^6)/(3^6))

The final answer is D.

Answer

16/243rd part of the population

Answer

32/243rd part of the population

Answer

32/729th part of the population

Answer

64/729th part of the population

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?

Explanation

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