Question

During one year, the population of town increased by 5\(\%\) .If the total population is 9975 at the end of the second year , then what was the population size in the beginning of the first year?

• A. 1000
• B. 10000
• C. 8500
• D. 9000

Answer 1

The Correct Option is B

Population Growth Calculation 

Let the population at the beginning of the first year be P.

Step 1: Population Increase After First Year

At the end of the first year, the population increases by 5%, so it becomes:

\[ P \times 1.05 \]

Step 2: Population Increase After Second Year

At the end of the second year, the population again increases by 5%, so it becomes:

\[ P \times 1.05 \times 1.05 = P \times 1.05^2 \]

Step 3: Given Population

We are given that the population at the end of the second year is 9975:

\[ P \times 1.05^2 = 9975 \]

Step 4: Solving for P

\[ P = \frac{9975}{1.1025} = 10000 \]

Thus, the population size at the beginning of the first year is 10,000.