Q12 2017, Statistics

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

यदि ऐसी कोई नीति है कि किसी समुदाय की एक-तिहाई (1/3) आबादी प्रति वर्ष एक स्थान को छोड़कर किसी दूसरे स्थान पर चली जाए, तो छठवें वर्ष के बाद उस समुदाय की शेष बची आबादी क्या होगी, यदि इस अवधि के दौरान जनसंख्या में आगे और कोई वृद्धि न हुई हो?

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

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