The present population of a town is 2,00,000. Its population increase by 10% in the first year and 15% in the second year. Find the population of the town at the end of the two years.

Answer

To find the population of the town at the end of two years, we will calculate the population after each year based on the given percentage increases.

### Step 1: Calculate the population after the first year
1. **Present Population**: 200,000
2. **Percentage Increase in the First Year**: 10%

Using the formula for population after one year:
\[ \text{Population after 1 year} = \text{Present Population} \times \left(1 + \frac{r}{100}\right) \]
where \( r = 10 \).

Substituting the values:
\[ \text{Population after 1 year} = 200,000 \times \left(1 + \frac{10}{100}\right) \]
\[ = 200,000 \times \left(1 + 0.10\right) \]
\[ = 200,000 \times 1.10 \]
\[ = 220,000 \]

### Step 2: Calculate the population after the second year
1. **Present Population for the Second Year**: 220,000 (which is the population after the first year)
2. **Percentage Increase in the Second Year**: 15%

Using the same formula for the second year:
\[ \text{Population after 2 years} = \text{Present Population} \times \left(1 + \frac{r}{100}\right) \]
where \( r = 15 \).

Substituting the values:
\[ \text{Population after 2 years} = 220,000 \times \left(1 + \frac{15}{100}\right) \]
\[ = 220,000 \times \left(1 + 0.15\right) \]
\[ = 220,000 \times 1.15 \]
\[ = 253,000 \]

### Final Result
The population of the town at the end of two years is **253,000**.

---