During a year, the population of a town increased by 8% and during the next year, the population decreased by 8%. If the total population is 9936 at the end of the second year, then what was the population in the beginning of the first year ?

Options

A. 15000
B. 10000
C. 18000
D. 22000

Answer

To solve the problem, we need to determine the initial population of the town before the changes in population occurred over the two years.

### Step-by-Step Solution:

1. **Let the initial population be \( P \)**.
- We denote the population at the beginning of the first year as \( P \).

2. **Calculate the population after the first year (increase by 8%)**:
- The population increases by 8%, so the population after the first year can be calculated as:
\[ \text{Population after Year 1} = P + 0.08P = 1.08P \]

3. **Calculate the population after the second year (decrease by 8%)**:
- Now, the population decreases by 8% from the population after the first year. The population after the second year is:
\[ \text{Population after Year 2} = 1.08P - 0.08(1.08P) = 1.08P \times (1 - 0.08) = 1.08P \times 0.92 \]
- Simplifying this gives:
\[ \text{Population after Year 2} = 1.08P \times 0.92 = 0.9936P \]

4. **Set the equation equal to the final population**:
- According to the problem, the population at the end of the second year is 9936. Therefore, we can set up the equation:
\[ 0.9936P = 9936 \]

5. **Solve for \( P \)**:
- To find \( P \), we divide both sides of the equation by 0.9936:
\[ P = \frac{9936}{0.9936} \]
- Calculating this gives:
\[ P = 10000 \]

6. **Conclusion**:
- The initial population at the beginning of the first year was \( 10000 \).

### Final Answer:
The population in the beginning of the first year was **10,000**.