A village's population grew by 10% during the first year and then declined by 10% in the following year. If the population after the second year is 7,920, what was the initial population at the start?

Explanation

Let the initial population be P. After a 10% increase, the population becomes P × 1.10. Next, it decreases by 10%, so the population becomes P × 1.10 × 0.90 = 0.99P. Given the final population is 7,920, we have 0.99P = 7,920, which gives P = 7,920 ÷ 0.99 = 8,000. Therefore, the initial population was 8,000.