population of a city decreases by 10% at the end of first year and increases by 10% at the end of second year and again decreases by 10% at the end of third year. if the population of the city at the end of third year is 4465, then what was the population of the city at the beginning of the first year?

Let's analyze the problem step by step.

Problem Restatement

• Population decreases by 1 at the end of the 1st year.
• Population increases by 1 at the end of the 2nd year.
• Population decreases by 1 at the end of the 3rd year.
• Population at the end of the 3rd year is 44.
• We want to find the initial population of the city before these changes.

Step-by-Step Solution

Let the initial population be P.

1. After 1st year: Population decreases by 1
   Population = P - 1

2. After 2nd year: Population increases by 1
   Population = (P - 1) + 1 = P

3. After 3rd year: Population decreases by 1
   Population = P - 1

Given that the population at the end of the 3rd year is 44, we have:

P−1=44P-1=44P−1=44

Solving for PPP:

P=44+1=45P=44+1=45P=44+1=45

Final Answer

The initial population of the city was 45.