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 possible 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. **Understand the Phenotypic Ratio**:
The phenotypic ratio given is 1:6:x:20:x:6:1. This means that there are various phenotypes represented in this ratio.

2. **Calculate the Total Ratio**:
To find the total number of parts in the ratio, we sum all the coefficients:
\[ 1 + 6 + x + 20 + x + 6 + 1 = 34 + 2x \]

3. **Determine the Total Number of Zygotes**:
For a polygenic trait controlled by three genes, the total number of zygotes can be calculated using the formula \( 4^n \), where \( n \) is the number of genes. Here, \( n = 3 \):
\[ 4^3 = 64 \]

4. **Set Up the Equation**:
Since the total number of phenotypes must equal the total number of zygotes, we set up the equation:
\[ 34 + 2x = 64 \]

5. **Solve for x**:
Rearranging the equation gives:
\[ 2x = 64 - 34 \]
\[ 2x = 30 \]
Dividing both sides by 2:
\[ x = 15 \]

6. **Conclusion**:
The possible value of x is 15.

### Final Answer:
The possible value of x is **15**.