The present population of a town is 26,010 and it increases annually at a rate of 2%. What was the population of the town two years ago?

Introduction / Context:
This question involves reverse calculation with compound growth. The population of a town grows every year by a fixed percentage, and we are given the present population. We must find the population two years ago by reversing the growth process. This is a typical example of reverse compound interest or population growth problems in quantitative aptitude.

Given Data / Assumptions:
- Present population of the town is 26,010.
- The population increases by 2 percent per year.
- We need to find the population two years ago, assuming the same growth rate each year and no migration effects.

Concept / Approach:
If P0 is the population two years ago and it grows at 2 percent per year, then after one year the population is P0 * 1.02, and after two years it is P0 * 1.02^2. We are given the final population after two years as 26,010. Therefore, we use the relation:
26,010 = P0 * (1.02)^2. We then solve for P0 by dividing 26,010 by (1.02)^2.

Step-by-Step Solution:
Let the population two years ago be P0. Growth rate per year = 2%, so growth factor per year = 1.02. After two years, population = P0 * 1.02 * 1.02 = P0 * (1.02)^2. Given that P0 * (1.02)^2 = 26,010. Compute (1.02)^2 = 1.0404. So, P0 = 26,010 / 1.0404. Evaluating this gives P0 = 25,000.

Verification / Alternative check:
Check forward. If the population two years ago was 25,000 and it grows at 2 percent per year, then after one year population becomes 25,000 * 1.02 = 25,500. After the second year, it becomes 25,500 * 1.02 = 26,010. This exactly matches the given present population, confirming that 25,000 is the correct population two years ago.

Why Other Options Are Wrong:
25,100, 25,200, 25,350, and 25,500: If any of these were used as the starting population, applying 2 percent growth for two years would not result exactly in 26,010. They lead to slightly higher or lower final values, so they are not correct.

Common Pitfalls:
A common mistake is to subtract 2 percent twice from the current population rather than reversing compound growth properly. Another error is to assume linear growth instead of multiplicative growth. When the growth rate is per year and depends on the current population, it always behaves like compound interest and must be handled with powers of the growth factor, not simple subtraction.

Final Answer:
The population of the town two years ago was 25,000 people.