GATE 2025 AR — Architecture – Question 44
City populations in 2001, 2011, 2021 were 52000, 76000, 120000. Using the geometric mean of decadal growth rates and geometric-increase projection, find 2031 population, to nearest integer.
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Correct answer: 179000 to 184000
Explanation
Decadal percentage increases are 24/52=0.461538 and 44/76=0.578947. Their geometric mean is√[(24/52)(44/76)]=0.516918. Applying that increase to 120000 gives 182030.15 people, rounding to 182030. This follows the requested geometric mean of growth rates; averaging the multiplicative growth factors is a different convention.