If in a row, Rohan is 10^th from left and Mukesh is 13^th from right and there are four persons in between Rohan and Mukesh, then find the maximum and minimum number of persons in the row.

The correct option is B: 27, 17.

Detailed Solution:

1. Rohan is 10th from the left, so his position from the left is 10.
2. Mukesh is 13th from the right, so his position from the right is 13.
3. There are 4 persons between Rohan and Mukesh.
4. We calculate the maximum and minimum possible number of persons in the row:

Step 1: Maximum Number of Persons

If Rohan and Mukesh do not overlap, their positions and the 4 people between them form a row: 
Total persons = Rohan's position + Mukesh's position + persons in between. 
Total = 10 + 13 + 4 = 27.

Step 2: Minimum Number of Persons

When Rohan and Mukesh overlap or have shared positions, the row length decreases: 
Total persons = Maximum persons (27) - persons overlapping (10 - 1 or 9 positions). 
Total = 27 - 10 = 17.

Concept Behind the Problem:

The problem is based on counting positions in a row with overlapping and non-overlapping scenarios. The maximum number occurs when there’s no overlap between the individuals, while the minimum occurs when their positions overlap as much as possible.