A polygenic trait is controlled by 3 genes A, B and C. In a cross AaBbCc `xx` AaBbCc, the phenotypic ratio of the offsprings was observed as :
`1:6xx:20xx:6:1` what is the possibe value of x?

Options

A. 3
B. 9
C. 15
D. 25

Answer

To solve the problem of finding the value of x in the given phenotypic ratio of a polygenic trait controlled by three genes (A, B, and C), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Cross**: The cross is between AaBbCc and AaBbCc. Each gene has two alleles, which means there are multiple combinations of these alleles in the offspring.

2. **Identifying the Number of Genes**: We have three genes (A, B, and C). For polygenic traits, the number of phenotypes can be determined using the formula \( 4^n \), where \( n \) is the number of genes.

3. **Calculating Total Phenotypes**:
- Here, \( n = 3 \) (for genes A, B, and C).
- Therefore, the total number of phenotypes \( = 4^3 = 64 \).

4. **Analyzing the Given Phenotypic Ratio**: The phenotypic ratio is given as:
- \( 1 : 6x : 20x : 6 : 1 \).

5. **Summing the Ratios**:
- The total ratio can be expressed as:
\[ 1 + 6x + 20x + 6 + 1 = 34 + 6x. \]

6. **Setting Up the Equation**:
- Since the total number of phenotypes is 64, we can set up the equation:
\[ 34 + 6x = 64. \]

7. **Solving for x**:
- Rearranging the equation gives:
\[ 6x = 64 - 34, \]
\[ 6x = 30, \]
\[ x = \frac{30}{6} = 5. \]

8. **Final Calculation**:
- The value of \( x \) is 5.

### Conclusion:
The possible value of \( x \) is **5**.

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