What will be the condition of the progeny if the father is normal, while the mother has one gene for haemophilia and one gene for colour blindness on one of the X chromosomes?

The correct option is: 50 per cent haemophilic and colour blind sons and 50% normal sons

To understand why this is correct, let us analyze the genetic genotypes of both parents and determine the outcomes for their offspring:

1. Genotypes of the parents:
- Father: The father is normal. Since males have one X chromosome and one Y chromosome, his genotype is:
$$X^{N}Y$$
(where $X^N$ represents an X chromosome with normal alleles for both blood clotting and colour vision).
- Mother: The mother has one gene for haemophilia (represented by $h$) and one gene for colour blindness (represented by $c$) on one of her X chromosomes. This means her other X chromosome is normal. Her genotype is:
$$X^{hc}{X}^N$$
(where $X^{hc}$ carries both mutant alleles, and $X^N$ carries the normal dominant alleles).

2. Gametes produced:
- The father produces two types of sperm cells: 50% carrying the $X^N$ chromosome and 50% carrying the $Y$ chromosome.
- The mother produces two types of egg cells: 50% carrying the $X^{hc}$ chromosome and 50% carrying the normal $X^N$ chromosome.

3. Punnett Square of the offspring:
Let us cross the gametes to find the genotypes and phenotypes of the progeny:
- Daughters (receiving $X^N$ from the father):
1. $X^{hc}{X}^N$ - Normal daughter carrying the genes (carrier).
2. $X^N{X}^N$ - Completely normal daughter.
All daughters (100%) will have normal vision and normal blood clotting because the father's normal $X^N$ chromosome provides dominant alleles that mask the recessive mutant genes.

- Sons (receiving $Y$ from the father):
1. $X^{hc}Y$ - Haemophilic and colour blind son (50% of the sons).
2. $X^{N}Y$ - Normal son (50% of the sons).
Since males have only one X chromosome, whatever alleles they receive on the X chromosome from their mother will be expressed. Thus, half of the sons will inherit the mutant X chromosome and be both haemophilic and colour blind, while the other half will inherit the normal X chromosome and be normal.

Conclusion:
The genetic cross results in 50% of the sons being haemophilic and colour blind, and 50% of the sons being normal.