A town has population 2,65,000 at the beginning of 1986. If the annual growth rate is 52 per thousand (i.e., 5.2% per year), find the population at the beginning of 1991.

Introduction / Context:
Year-on-year percentage growth compounds. Over 5 years (from the start of 1986 to the start of 1991), the population multiplies by (1 + r)^5 with r = 5.2% = 0.052.

Given Data / Assumptions:

• Initial population P0 = 2,65,000.
• Annual growth rate r = 0.052 (52 per thousand).
• Years n = 5.

Concept / Approach:

• Population after n years: Pn = P0(1 + r)^n.
• Round to the nearest hundred as per common exam convention if needed.

Step-by-Step Solution:

Verification / Alternative check:
Using a more precise value (1.052)^5 ≈ 1.28936 gives ≈ 3,41,690; among the options, 3,41,400 is the nearest standard rounded choice.

Why Other Options Are Wrong:

• 3,40,400 and 3,42,400 are farther from the precise computation; 3,43,400 overshoots.

Common Pitfalls:

• Treating the growth as linear (simple increase) instead of compound.

Final Answer:
3,41,400