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?
Answer & explanation
Answer: (d) 64/729th part of the population
Each year one-third leaves, so two-thirds of the previous year's population remains. The fraction compounds, so after six years the population left is (2/3)⁶ = 64/729 of the original.
- After one year, 1 − 1/3 = 2/3 of the population remains.
- The same fraction applies to what is left each year, so after 6 years the remainder is (2/3)⁶.
- (2/3)⁶ = 2⁶/3⁶ = 64/729.
- Check: the denominator must be 3⁶ = 729 and the numerator 2⁶ = 64; only (d) has both.
Remember · Repeated fractional loss compounds: after n rounds of losing 1/k, the remainder is (1 − 1/k)ⁿ, not 1 − n/k.
Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·