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 AaBb, the ratio of characters x,y and z seen in its offsprings is

Options

A. Option1 `3:4:9`
B. Option2 `3:1:12`
C. Option3 `1:12:3`
D. Option4 `9:4:3`

Answer

To solve the problem, we need to analyze the genetic interactions between the alleles and how they express different characters based on the given genotypes.

### Step-by-Step Solution:

1. **Identify the Genes and Alleles**:
- Gene B has two alleles: B (dominant) and b (recessive).
- B expresses character X, while b expresses character Y.
- Gene A is epistatic over gene B, meaning that when A is dominant (A), it suppresses the expression of both B and b, resulting in character Z. When A is recessive (a), the expression of B and b is allowed.

2. **Determine the Genotypes of the Parents**:
- Both parents have the genotype AaBb.

3. **Gamete Formation**:
- Each parent can produce four types of gametes due to independent assortment:
- AB
- Ab
- aB
- ab

4. **Punnett Square Setup**:
- Create a Punnett square using the gametes from both parents:
```
| | AB | Ab | aB | ab |
|---|----|----|----|----|
| AB| AABB | AABb | AaBB | AaBb |
| Ab| AABb | AAbb | AaBb | Aabb |
| aB| AaBB | AaBb | aaBB | aaBb |
| ab| AaBb | Aabb | aaBb | aabb |
```

5. **Determine the Phenotypes**:
- For each genotype, determine the resulting phenotype:
- **AABB, AABb, AaBB, AaBb**: All have at least one dominant A, so they express character Z.
- **AAbb, Aabb**: These have one recessive a, so they express character Y.
- **aaBB, aaBb**: These have two recessive a's, allowing B to express character X.
- **aabb**: This genotype expresses character Y.

6. **Count the Phenotypes**:
- Count the occurrences of each character:
- Character Z (A_): 12 occurrences (AABB, AABb, AaBB, AaBb)
- Character X (aaB): 3 occurrences (aaBB, aaBb)
- Character Y (Aabb, aabb): 1 occurrence (Aabb, aabb)

7. **Calculate the Ratio**:
- The ratio of characters X, Y, and Z in the offspring is:
- Character X : Character Y : Character Z = 3 : 1 : 12

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