The population of a village is 10000. If the population increase by 10% in the first year, by 20% in the second year and due to mass exodus it decreases by 5% in the third year, what will be its population after 3 years

Answer

To find the population of the village after 3 years, we will calculate the population at the end of each year based on the percentage increases and decrease provided.

### Step-by-Step Solution:

1. **Initial Population**:
- The initial population of the village is given as \( P = 10,000 \).

2. **First Year Population Increase**:
- The population increases by 10% in the first year.
- To calculate the population after the first year:
\[ \text{Population after Year 1} = P \times \left(1 + \frac{10}{100}\right) = 10,000 \times 1.10 = 11,000 \]

3. **Second Year Population Increase**:
- The population increases by 20% in the second year.
- To calculate the population after the second year:
\[ \text{Population after Year 2} = 11,000 \times \left(1 + \frac{20}{100}\right) = 11,000 \times 1.20 = 13,200 \]

4. **Third Year Population Decrease**:
- The population decreases by 5% in the third year.
- To calculate the population after the third year:
\[ \text{Population after Year 3} = 13,200 \times \left(1 - \frac{5}{100}\right) = 13,200 \times 0.95 = 12,540 \]

5. **Final Population**:
- The final population after 3 years is \( 12,540 \).

### Final Answer:
The population of the village after 3 years will be **12,540**.

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