A gene has two alleles B and b. B is responsible for the expression of character x . b. is responsible for the expression of character y. B. is completely dominant over b. Another gene A is epistatic on gene B. When A is in the dominant condition it suppress the expression of B and b and gives rise to character z.In recessive condition (allele a) allows expression of B and b. When an organism with genotype AaBb is crossed with another organism with genotype AbBb, the ratio of characters x,y and z seen in its offsprings is

Options

A. `3:4:9`
B. `3:1:12`
C. `1:12:3`
D. `9:4:3`

Answer

To solve the problem, we need to analyze the genetic cross between two organisms with the genotypes AaBb and AaBb. We will determine the phenotypic ratios of characters X, Y, and Z in their offspring.

### Step 1: Identify the alleles and their effects
- Allele B (dominant) expresses character X.
- Allele b (recessive) expresses character Y.
- Allele A (dominant) is epistatic to B, meaning it suppresses the expression of both B and b and expresses character Z when present in a dominant form (AA or Aa).
- Allele a (recessive) allows the expression of B and b.

### Step 2: Set up the cross
We are crossing two organisms with the genotype AaBb:
- Parent 1: AaBb
- Parent 2: AaBb

### Step 3: Create a Punnett square
To find the offspring's genotypes, we will create a Punnett square for the alleles A/a and B/b.

1. **Gametes from Parent 1 (AaBb)**: AB, Ab, aB, ab
2. **Gametes from Parent 2 (AaBb)**: AB, Ab, aB, ab

Now we can fill in the Punnett square:

| | AB | Ab | aB | ab |
|---------|--------|--------|--------|--------|
| **AB** | AABB | AABb | AaBB | AaBb |
| **Ab** | AABb | AAbb | AaBb | Aabb |
| **aB** | AaBB | AaBb | aaBB | aaBb |
| **ab** | AaBb | Aabb | aaBb | aabb |

### Step 4: Determine phenotypes from genotypes
Now we will analyze the resulting genotypes to determine the phenotypes:

- **AABB, AABb, AaBB, AaBb**: All these genotypes have at least one dominant A, so they express character Z.
- **AAbb, Aabb**: These genotypes have one dominant A and one recessive b, so they express character Z.
- **aaBB, aaBb**: These genotypes have no dominant A, so they express character X (since B is dominant).
- **aabb**: This genotype expresses character Y (since both A and B are recessive).

### Step 5: Count the phenotypes
From the Punnett square, we can count the phenotypes:
- Character Z (A present): 12 occurrences (AABB, AABb, AaBB, AaBb, AABb, AAbb, AaBb, AaBb, AaBb, AaBb, AaBb, AaBb)
- Character X (B present, A absent): 3 occurrences (aaBB, aaBb)
- Character Y (b present, A absent): 1 occurrence (aabb)

### Step 6: Write the final ratio
The final ratio of characters X, Y, and Z in the offspring is:
- X: 3
- Y: 1
- Z: 12

Thus, the ratio is **3:1:12**.

### Final Answer
The ratio of characters X, Y, and Z seen in the offspring is **3:1:12**.