The number of chromosomes in parents and offspring of particular species remain constant due to meiosis. Meiosis is a type of cell division that occurs in the reproductive cells of an organism to form gametes which has half the DNA component of the parents. When the male and female gametes fuse to form the zygote, the DNA is restored to the normal complement. Hope it helps.
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The chromosome number in the parents and their off-springs is equal because a reduction division known as meiotic cell division takes place in the reproductive cells of the parents .
4 daughter cells are formed in the end of meiotic division.