Census population of a district in 1981 was 4.54 Lakhs, while in year 2001 it…

Concept: When a population grows at a roughly steady (linear) rate, the average annual increase between two known census years is (later population − earlier population) ÷ (number of years between them). To estimate the population in a later year, multiply this per-year rate by the number of years elapsed since the last known census and add it to that census figure.

1. Years between the two known census figures: 2001 − 1981 = 20 years.

2. Total increase over those 20 years: 7.44 − 4.54 = 2.90 lakhs.

3. Average annual increase: 2.90 ÷ 20 = 0.145 lakhs per year.

4. Years from the last known census (2001) to the target year (2009): 2009 − 2001 = 8 years.

5. Increase over those 8 years: 8 × 0.145 = 1.16 lakhs.

6. Estimated 2009 population: 7.44 + 1.16 = 8.60 lakhs.

Cross-check: applying the same annual rate across the full 1981-to-2009 span of 28 years gives 28 × 0.145 = 4.06 lakhs; adding this to the 1981 population gives 4.54 + 4.06 = 8.60 lakhs — the same result, confirming the estimate.

So the estimated population of the district in 2009 is 8.60 lakhs.