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 determining the possible value of x in the phenotypic ratio \(1:6x:20x:6:1\) for a polygenic trait controlled by three genes (A, B, and C), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Phenotypic Ratio**:
The given phenotypic ratio is \(1:6x:20x:6:1\). This means that the total number of phenotypes can be expressed in terms of x.

2. **Calculating the Total Ratio**:
To find the total ratio, we can sum the coefficients:
\[ 1 + 6x + 20x + 6 + 1 = 2 + 26x \]

3. **Setting Up the Equation**:
The total ratio must equal the total number of phenotypes produced by the cross. Since we are dealing with a polygenic trait influenced by three genes, we can determine the total number of phenotypes as \(n + 1\), where \(n\) is the number of genes. In this case, \(n = 3\), so the total number of phenotypes is \(3 + 1 = 4\).

4. **Equating and Solving for x**:
We can set the total ratio equal to the number of phenotypes:
\[ 2 + 26x = 4 \]
Rearranging gives:
\[ 26x = 4 - 2 \]
\[ 26x = 2 \]
\[ x = \frac{2}{26} = \frac{1}{13} \]

5. **Finding the Possible Values of x**:
However, we need to find integer values for x that fit the ratio \(1:6x:20x:6:1\). The options given are 3, 9, 15, or 25. We can substitute these values into the ratio to check which one satisfies the condition.

- For \(x = 3\):
\[ 1:6(3):20(3):6:1 = 1:18:60:6:1 \]
- For \(x = 9\):
\[ 1:6(9):20(9):6:1 = 1:54:180:6:1 \]
- For \(x = 15\):
\[ 1:6(15):20(15):6:1 = 1:90:300:6:1 \]
- For \(x = 25\):
\[ 1:6(25):20(25):6:1 = 1:150:500:6:1 \]

6. **Identifying the Correct Value**:
The correct value of x that maintains the ratio consistent with the observed phenotypic distribution is \(x = 15\).

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