The population of a village decreases at the rate of 20- % per annum. If its polulation 2 years ago was 10,000 the present propulation is

Options

A. 4600
B. 6400
C. 7600
D. 6000

Answer

To find the present population of the village, we will follow these steps:

### Step 1: Understand the decrease in population
The population of the village decreases at a rate of 20% per annum. This means that each year, the population retains 80% of its value from the previous year.

### Step 2: Convert the percentage to a fraction
The fraction representing the remaining population after a 20% decrease is:
\[ 1 - 0.20 = 0.80 \]
This can also be expressed as:
\[ \frac{80}{100} = \frac{4}{5} \]

### Step 3: Calculate the population after the first year
If the population 2 years ago was 10,000, we can calculate the population after the first year (1 year ago) using the fraction:
\[ \text{Population after 1 year} = \text{Population 2 years ago} \times \frac{4}{5} \]
\[ = 10,000 \times \frac{4}{5} = 10,000 \times 0.8 = 8,000 \]

### Step 4: Calculate the population after the second year
Now, we will calculate the population after the second year (present population) using the same fraction:
\[ \text{Present Population} = \text{Population after 1 year} \times \frac{4}{5} \]
\[ = 8,000 \times \frac{4}{5} = 8,000 \times 0.8 = 6,400 \]

### Final Answer
The present population of the village is:
\[ \boxed{6,400} \]

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