The correct option is R - S - T.

To determine the correct order of the genes on the chromosome, we can use the concept of gene mapping. In genetic mapping, the recombination frequency (recombinant percentage) between two genes is directly proportional to the physical distance between them on the chromosome. One percent of recombination is equivalent to one map unit (mu) or centimorgan (cM).

Based on the given data, we can represent the distances between the genes as follows:
1. The distance between genes R and S is 20% recombination, which corresponds to 20 map units.
2. The distance between genes R and T is 35% recombination, which corresponds to 35 map units.
3. The distance between genes S and T is 15% recombination, which corresponds to 15 map units.

Now, we look for the two genes that are furthest apart to define the outer boundaries of our map. The largest distance is between R and T (35 map units). This indicates that R and T are the outermost genes:
R ----------------------------------------- 35 map units ----------------------------------------- T

Next, we place the third gene, S, in relation to the outer genes R and T. We are given:
- The distance between R and S is 20 map units.
- The distance between S and T is 15 map units.

If gene S lies between R and T, the sum of the distances from R to S and from S to T must equal the total distance between R and T:

$$\text{Distance(R - S)}+\text{Distance(S - T)}=\text{Distance(R - T)}$$

Substituting the given values:

$$20\text{ map units}+15\text{ map units}=35\text{ map units}$$

Since the addition holds true ($20+15=35$), gene S must be positioned between genes R and T.

Therefore, the sequence of the genes on the chromosome is R - S - T.