In a Random mating population of `28,800` individuals percentage of dominant homozygous individuals is `49%` find out the precentage of heterozygous individual -

Options

A. `21%`
B. `42%`
C. `32%`
D. `9%`

Answer

To solve the problem step by step, we will use the Hardy-Weinberg principle, which provides a mathematical framework for understanding the genetic variation in a population.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Total population = 28,800 individuals
- Percentage of dominant homozygous individuals (AA) = 49%

2. **Convert Percentage to Decimal**:
- The frequency of dominant homozygous individuals (p²) = 49% = 0.49

3. **Use the Hardy-Weinberg Equation**:
- The Hardy-Weinberg equation is:
\[ p^2 + 2pq + q^2 = 1 \]
- Here, \( p^2 \) is the frequency of homozygous dominant (AA), \( 2pq \) is the frequency of heterozygous (Aa), and \( q^2 \) is the frequency of homozygous recessive (aa).

4. **Calculate the Frequency of Dominant Allele (p)**:
- Since \( p^2 = 0.49 \), we can find \( p \) by taking the square root:
\[ p = \sqrt{0.49} = 0.7 \]

5. **Calculate the Frequency of Recessive Allele (q)**:
- Using the relationship \( p + q = 1 \):
\[ q = 1 - p = 1 - 0.7 = 0.3 \]

6. **Calculate the Frequency of Heterozygous Individuals (2pq)**:
- Now, substitute the values of \( p \) and \( q \) into the equation for heterozygous frequency:
\[ 2pq = 2 \times 0.7 \times 0.3 = 0.42 \]

7. **Convert Frequency to Percentage**:
- To find the percentage of heterozygous individuals, convert the frequency to percentage:
\[ \text{Percentage of heterozygous individuals} = 0.42 \times 100 = 42\% \]

### Final Answer:
The percentage of heterozygous individuals in the population is **42%**.

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