In cucumbers dull fruit D is dominant to glossy fruit d and

In cucumbers, dull fruit (D) is dominant to glossy fruit (d), and orange fruit (R) is dominant to cream (r) fruit. The gene that codes for dull versus glossy assorts independently from the gene that codes for orange versus cream. A plant that has dull and orange fruits is crossed to a plant that has dull and cream fruits. The cross produces ³₈ plants with dull and orange fruits, ³₈ plants with dull and cream fruits, ¹₈ plants with glossy and orange fruits, and ¹₈ plants with glossy and cream fruits. Give the genotypes of the parents and offspring of the cross.

Solution

Let us designate each allele first -

Dull Fruit - D
Glossy Fruit -d
Orange Fruit - R
Cream Fruit - r

Additionally, Dull (D) is dominant to Glossy (d), and
Orange (R) is dominant to Cream (r)

Now, a cross is made between a plant that has dull and orange fruits to a plant that has dull and cream fruits. Therefore, we can try to analyze possible genotypes of the parents.

Parent 1 is Dull and Orange. That means it will have atleast one \'D\' and one \'R\'. The possible combinations therefore could be -
DDRR
DdRR
DdRr

Parent 2 is Dull and Cream. This means that it will have atleast one \'D\' and both \'r\' ( since cream phenotype will be expressed only in homozygous recessive condition). The possible genotypes therefore could be -

DDrr
Ddrr

Now we have possible genotypes, let us try to cross the genotypes to see which cross will give us the result as described in the question. The genotype crosses can be as follows -

1)
DDRR X DDrr
This will segregate as - DR X Dr, which will lead to the genotype DDRr.
Therefore, in the first cross, it is evident that only one genotype and phenotype will be produced.

2)
DdRR X DDrr
This will segregate as DR and dR on the first parent, and Dr on the second parent. The F1 progeny will have either of the two genotypes- DDRr or DdRr. Since this does not qualify for the conditions set in the question, we can rule out this type of parental genotype.

3)
DdRr X DDrr
This will segregate as DR, Dr, dR and dr on the first parent; and as Dr on the second parent.
The probable genotypes would be DDRr, DDrr, DdRr and Ddrr.
The phenotypes are:
DDRR- Dull, Orange
DDrr - Dull, Cream
DdRr - Dull, Orange,
Ddrr - Dull, Cream

The above phenotype does not satisfy our condition, and hence we can reject the parental genotypes.

4)
DdRR X Ddrr
The above will segregate as DR and dR on the first parent, and as Dr and dr on the second parent.
The possible genotypes would be DDRr, DdRr, DdRr and ddRr. The phenotypes would be-
DDRr - Dull, Orange
DdRr - Dull, Orange
ddRr - Glossy, Orange.
The above phenotype does not satisfy our condition, and hence we can reject the parental genotypes.

5)
DdRr X Ddrr
The above will segregate as DR, Dr, dR and dr on the first parent; and as Dr and dr on the second parent.
The possible genotypes would be-

The total number of phenotypes = 8

Ratio of phenotypes -

Dull, Orange = 3/8
Dull, Cream = 3/8
Glossy, Orange = 1/8
Glossy, Cream = 1/8

This satisfies the condition given in the question.

Therefore the genotypes of the parents are DdRr and Ddrr.