Answer: 25 of the chicks will be black
Explanation: Since the chickens are intermediate in colour, that is they are not black, they are heterozygous. Let B represent the allele for black colour and B represent the allele for blue colour, therefore the genotype of a chicken with an intermediate colour is Bb. A cross between two Bb chicken will produce 1 BB, 2 Bb and 1 bb chicks. 1 BB will manifest outwardly as black, 2Bb will manifest outwardly as intermediate colored while 1 bb will manifest outwardly as blue colored chicks.
Since one out of four chicks are black colored, if the two chicken produced 100 chicks, the number of chicks that will be black is 1/4 x 100 = 25. Therefore, 25 chicks out of 100 will be black.
See the attached punnet square for more information