Question

In Drosophila , genes for wing shape (wild type, arc) and the gene for body colour (wild type, black) are located on the same chromosome. A test cross was performed between a fly heterozygous for both wing shape and body colour with another fly homozygous for both traits. The cross resulted in a number of offsprings is as follows-

No of offspring	Trait
682	Wild type
517	Black
489	Arc shape
716	Arc-black

How many linkage map units apart are these two genes?
A. 5.8 LMU
B. 42 LMU
C. 58 LMU
D. It is not possible to determine from the data given.

Answer 1

Genetics is the study of the transition ("inherited") of traits such as hair colour, eye colour, and risk of disease from parents to their offspring. Genetics affect the way these inherited characteristics can vary from person to person.

Formula used: $Recombination\text{ }frequency=Total\text{ }no.\text{ }of\text{}recombinants/Total\text{ }no.\text{ }of\text{ }offsprings*100$

Complete answer:
A gene, an inherited information unit that occupies a fixed location on a chromosome (locus). One of two or more copies of a gene is an allele, if genes are located on separate chromosomes or far apart on the same chromosome, they are assorted separately and are considered to be unlinked. They are said to be linked when genes are close together on the same chromosome.
Crossing over is the interchange of genetic material that happens during the development of egg and sperm cells, aligning paired chromosomes from each parent so that the paired chromosomes cross identical DNA sequences over each other.
In genetics, recombination happens through the phenomenon of crossing over, the primary mechanism through which variation is introduced into populations. Thus offsprings are produced, some receive phenotype similar to their parents while some offsprings are different from both the parents. These different offsprings have genotype different from their parents are called recombinants. The frequency with which recombinants are produced is called recombinant frequency.
The mechanism by which we determine the position of genes along a given chromosome is gene mapping. Which is given in map units called special units. Map units can be calculated by the percent recombination (recombination frequency) measurement on the chromosome between the two genes. One percent recombination equals one unit of a map, two percent recombination equals two units of a map, and so on.
In our case let us assume that the gene for wing shape be Ss where S is wild type normal shape whiles is the allele for arc shape. Gene for body colour is Cc where C is the allele for wild type brown colour while c is the allele for black colour. When the cross is performed between heterozygous father having genotype SsCc and homozygous mother having genotype sscc.

Thus four offsprings are produced.
SsCc - Wild type
Sscc - Black
ssCc - arc shape
sscc - arc black

Thus, here four types of offspring are produced; all of them are unequal in number, indicating that genes are located on the same chromosome.

Now, recombinants that have different phenotypes from their parents are Black (Sscc) and arc shape (ssCc). Now let us first calculate the number of recombinants,
Black Recombinants= 517
Arc shape recombinants = 489
No of recombinants = 517+489=1006
Total no. of offspring= 682+517+489+716=2404
Putting values in formula : $\begin{aligned} & Recombination\text{ }frequency=Total\text{ }no.\text{ }of\text{ }recombinants/Total\text{ }no.\text{ }of\text{ }offsprings*100 \\\ & =\frac{1006}{2402}\times 100 \\\ & =\text{ }0.418\text{ }\times 100~ \\\ & ~=\text{ }41.8 \end{aligned}$
Since, we have seen above that recombination of one percent equals one map unit, a recombination of two percent equals two map units, and so on. Thus, 41.8 percent of recombination is equal to 41.8 map units. which is equivalent to 42 LMU. Thus, from the above discussion, we come to the conclusion that these two genes are 42LMU units apart.
Thus, the correct answer is option B, i.e., 42LMU.

Note: For each gene, a human inherits two alleles, one from each parent. When the two alleles are the same, for that gene, the person is homozygous. The person is heterozygous for that gene if the alleles are different.