If the population of a village increases in first two years by 15% and 10% respectively and then decreases by 10% for one more year, then find overall increase percentage in population

Options

A. 12.25%
B. 13.85%
C. 18.65%
D. 15.75%

Answer

To solve the problem of calculating the overall percentage increase in the population of a village after a series of percentage changes, we can follow these steps:

### Step-by-Step Solution:

1. **Assume Initial Population**:
Let's assume the initial population of the village is 100.

2. **Calculate Population After First Increase (15%)**:
- Increase = 15% of 100 = \( \frac{15}{100} \times 100 = 15 \)
- New Population = Initial Population + Increase = \( 100 + 15 = 115 \)

3. **Calculate Population After Second Increase (10%)**:
- Increase = 10% of 115 = \( \frac{10}{100} \times 115 = 11.5 \)
- New Population = Previous Population + Increase = \( 115 + 11.5 = 126.5 \)

4. **Calculate Population After Decrease (10%)**:
- Decrease = 10% of 126.5 = \( \frac{10}{100} \times 126.5 = 12.65 \)
- New Population = Previous Population - Decrease = \( 126.5 - 12.65 = 113.85 \)

5. **Calculate Overall Increase in Population**:
- Increase = Final Population - Initial Population = \( 113.85 - 100 = 13.85 \)

6. **Calculate Overall Percentage Increase**:
- Percentage Increase = \( \left( \frac{Increase}{Initial Population} \right) \times 100 = \left( \frac{13.85}{100} \right) \times 100 = 13.85\% \)

### Final Answer:
The overall percentage increase in the population is **13.85%**.