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?
- (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 ✓ UPSC's answer
Why the answer is (d)
• Each year one-third of the remaining population leaves, so two-thirds stays.
• After six years the fraction left is (2/3) multiplied by itself six times: 2⁶/3⁶ = 64/729.
• So 64/729 of the population remains, option (d).
Why the other options are wrong
- (a) 16/243rd part of the population
- 16/243 is not (2/3) raised to the sixth power; (2/3)⁶ = 64/729.
- (b) 32/243rd part of the population
- 32/243 = (2/3)⁵, the fraction left after five years, not six.
- (c) 32/729th part of the population
- 32/729 has the wrong numerator: 2⁶ = 64, not 32.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.