The population of a particular area A of a city is 5000. It increases by 10% in 1st yr. It decreases by 20% in the 2nd yr because of some reason. In the 3rd yr, the population increases by 30%. What will be the population of area A at the end of 3 yr ?

Answer

To find the population of area A at the end of 3 years, we will calculate the population at the end of each year based on the given percentage increases and decreases.

### Step-by-Step Solution:

1. **Initial Population**:
The initial population of area A is given as 5000.

2. **Population after 1st Year**:
- The population increases by 10% in the first year.
- To calculate the increase:
\[ \text{Increase} = \text{Initial Population} \times \frac{10}{100} = 5000 \times 0.10 = 500 \]
- Therefore, the population at the end of the first year is:
\[ \text{Population after 1st Year} = 5000 + 500 = 5500 \]

3. **Population after 2nd Year**:
- The population decreases by 20% in the second year.
- To calculate the decrease:
\[ \text{Decrease} = \text{Population after 1st Year} \times \frac{20}{100} = 5500 \times 0.20 = 1100 \]
- Therefore, the population at the end of the second year is:
\[ \text{Population after 2nd Year} = 5500 - 1100 = 4400 \]

4. **Population after 3rd Year**:
- The population increases by 30% in the third year.
- To calculate the increase:
\[ \text{Increase} = \text{Population after 2nd Year} \times \frac{30}{100} = 4400 \times 0.30 = 1320 \]
- Therefore, the population at the end of the third year is:
\[ \text{Population after 3rd Year} = 4400 + 1320 = 5720 \]

5. **Final Result**:
The population of area A at the end of 3 years is **5720**.