Question

If there is a policy that 1/3rd of a 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?

Answer 1

Answer:

32/243th of the initial population

Step-by-step explanation:

Hi,

Let 'x' be the initial population in the given community,

Given that 1/3rd are migrated i.e., x/3,

so remaining population in that community at the end of the year would be

= x - x/3 = 2x/3,

remaining population in that community at the end of the second year would be

= x - x/3 = 2/3*2x/3 = 4x/9.

Continuing so on, we can observe that the count of remaining population at

the end of each year forms a geometric progression with x being the first

term and 2/3 being the common ratio,

hence nth term for the above G.P would be a.rⁿ⁻¹,

where a is first teerm = x

r = common ratio = 2/3

=>Population remaining at the end of 6th year would be

= x(2/3)⁶⁻¹

=32x/243.

So, 32/243th of the initial population would be left

Hope, it helped !

Hope, it helped!