Three years ago, the population of a town was 50000. If the annual increase during three sucessive years be at the rate of 5%, 4% and 3% respectively, what is its present population?

Answer

To find the present population of the town, we will calculate the population after each year using the given rates of increase. Here’s the step-by-step solution:

### Step 1: Identify the initial population and rates of increase
- Initial population (3 years ago) = 50,000
- Rate of increase for Year 1 = 5%
- Rate of increase for Year 2 = 4%
- Rate of increase for Year 3 = 3%

### Step 2: Calculate the population after Year 1
The formula to calculate the population after a year with a percentage increase is:
\[ \text{New Population} = \text{Old Population} \times \left(1 + \frac{\text{Rate}}{100}\right) \]

For Year 1:
\[ \text{Population after Year 1} = 50,000 \times \left(1 + \frac{5}{100}\right) \]
\[ = 50,000 \times 1.05 \]
\[ = 52,500 \]

### Step 3: Calculate the population after Year 2
For Year 2:
\[ \text{Population after Year 2} = 52,500 \times \left(1 + \frac{4}{100}\right) \]
\[ = 52,500 \times 1.04 \]
\[ = 54,600 \]

### Step 4: Calculate the population after Year 3
For Year 3:
\[ \text{Population after Year 3} = 54,600 \times \left(1 + \frac{3}{100}\right) \]
\[ = 54,600 \times 1.03 \]
\[ = 56,238 \]

### Conclusion
The present population of the town is **56,238**.

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