In a breeding experiment between two parents showing the dominant and the recessive phenotype of the character the offspring showed equal proportions of the dominant and recessive phenotypes. Which one of following statement must be true?

Options

A. Both the parents has equal number of genes for the character
B. Both the parents carried recessive genes
C. Both the parents were true breeding
D. all are true

Explanation

To solve the question regarding the breeding experiment between two parents showing dominant and recessive phenotypes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Dominant and Recessive Phenotypes**:
- In genetics, dominant phenotypes are expressed when at least one dominant allele is present, while recessive phenotypes are expressed only when two recessive alleles are present.

2. **Analyzing the Offspring's Phenotypes**:
- The problem states that the offspring showed equal proportions of dominant and recessive phenotypes. This indicates that the offspring are exhibiting a 1:1 ratio of dominant to recessive traits.

3. **Determining Parental Genotypes**:
- For a 1:1 ratio of dominant to recessive phenotypes in the offspring, the most likely scenario is that one parent is homozygous dominant (e.g., TT) and the other parent is homozygous recessive (e.g., tt).
- However, if both parents are showing dominant and recessive phenotypes, they must be heterozygous (e.g., Tt) for the dominant trait, allowing for the expression of both phenotypes in the offspring.

4. **Using a Punnett Square**:
- Construct a Punnett square with both parents being heterozygous (Tt x Tt). The resulting genotypes will be:
- TT (homozygous dominant)
- Tt (heterozygous dominant)
- Tt (heterozygous dominant)
- tt (homozygous recessive)
- This results in a phenotypic ratio of 3:1 (3 dominant: 1 recessive).

5. **Conclusion**:
- Since the offspring showed equal proportions of dominant and recessive phenotypes, it indicates that both parents must carry the recessive allele. Therefore, the correct statement is that both parents carried the recessive genes.

### Final Answer:
The statement that must be true is: **Both parents carried the recessive genes.**

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