Laxmangarh population every year `4%` increase . If population after `2` year `67600` then find present population.

Options

A. `62500`
B. `63600`
C. `60,500`
D. `65,600`

Answer

To find the present population of Laxmangarh given that it increases by 4% every year and that the population after 2 years is 67,600, we can follow these steps:

### Step 1: Define the Present Population
Let the present population be represented as \( X \).

### Step 2: Calculate the Population After 1 Year
After 1 year, the population increases by 4%. Therefore, the population at the end of the first year can be calculated as:
\[ \text{Population after 1 year} = X + 0.04X = 1.04X \]

### Step 3: Calculate the Population After 2 Years
At the end of the second year, the population again increases by 4%. Thus, the population at the end of the second year is:
\[ \text{Population after 2 years} = 1.04X + 0.04(1.04X) = 1.04X \times 1.04 = (1.04)^2 X \]
Calculating \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]
So, the population after 2 years can be expressed as:
\[ \text{Population after 2 years} = 1.0816X \]

### Step 4: Set Up the Equation
We know from the problem that the population after 2 years is 67,600. Therefore, we can set up the equation:
\[ 1.0816X = 67600 \]

### Step 5: Solve for Present Population \( X \)
To find \( X \), we can rearrange the equation:
\[ X = \frac{67600}{1.0816} \]
Calculating this gives:
\[ X = 62499.999 \approx 62500 \]

### Conclusion
Thus, the present population of Laxmangarh is approximately **62,500**.

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