The population of Varanasi is 2,25,000. If the annual birth rate and death rate are 9 % and 7 %, calculate the population of city after 2 years.

Options

A. 432090
B. 423900
C. 243090
D. 234090

Answer

To solve the problem of calculating the population of Varanasi after 2 years given the initial population, birth rate, and death rate, we can follow these steps:

### Step 1: Identify the initial population
The initial population of Varanasi is given as:
\[ \text{Initial Population} = 2,25,000 \]

### Step 2: Calculate the net growth rate
The annual birth rate is 9% and the annual death rate is 7%. To find the net growth rate, we subtract the death rate from the birth rate:
\[ \text{Net Growth Rate} = \text{Birth Rate} - \text{Death Rate} \]
\[ \text{Net Growth Rate} = 9\% - 7\% = 2\% \]

### Step 3: Calculate the population after 1 year
To find the population after 1 year, we can use the formula:
\[ \text{Population after 1 year} = \text{Initial Population} \times \left(1 + \frac{\text{Net Growth Rate}}{100}\right) \]
Substituting the values:
\[ \text{Population after 1 year} = 2,25,000 \times \left(1 + \frac{2}{100}\right) \]
\[ \text{Population after 1 year} = 2,25,000 \times 1.02 \]
\[ \text{Population after 1 year} = 2,29,500 \]

### Step 4: Calculate the population after 2 years
Now, we will use the population after 1 year to find the population after the second year using the same growth rate:
\[ \text{Population after 2 years} = \text{Population after 1 year} \times \left(1 + \frac{\text{Net Growth Rate}}{100}\right) \]
Substituting the values:
\[ \text{Population after 2 years} = 2,29,500 \times 1.02 \]
\[ \text{Population after 2 years} = 2,33,490 \]

### Final Answer
The population of Varanasi after 2 years is:
\[ \text{Final Population} = 2,33,490 \]

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