What is the sum of the number of bags of the persons who sits at the extreme ends?

Study the following information carefully and answer the questions given below:

Six persons – A, B, C, D, E and F sit in a row and all are facing north but not in same order as given. Each of them has different number of bags. None of them has bags less than 15 and more than 60. Only two persons sit between E and the one who has 35 bags, and neither of them sits at the extreme ends. The number of persons sitting to the right of E is one less than the number of persons sitting to the left of A. The one who has two bags less than C sits second to the left of A who sits adjacent to C. F sits to the immediate right of D who has even square number of bags. A has 18 bags less than B who has 20 bags more than D. E has prime number of bags and 15 bags more than the one who sits two places away from B.

To find the sum of the number of bags of the persons sitting at the extreme ends, let us step-by-step determine the seating arrangement and bag counts of all six persons (A, B, C, D, E, and F) in positions 1 to 6 from left to right facing North.

Step 1: Determine the Seating Arrangement

1. Position of E and 35-bag holder:
Only two persons sit between E and the person with 35 bags, and neither sits at the extreme ends (positions 1 and 6). Therefore, E and the 35-bag holder must occupy positions 2 and 5.
2. Position of A:
The number of persons to the right of E is one less than the number of persons to the left of A. Placing E at position 2 gives 4 persons to its right, meaning A must have 5 persons to its left. Thus, A sits at position 6.
3. Positions of C, D, F, and B:
- A is adjacent to C, so C sits at position 5 (and has 35 bags).
- The person second to the left of A (position 4) has 2 bags less than C, which equals $35-2=33$ bags.
- F sits to the immediate right of D, occupying adjacent empty spots at positions 3 and 4 respectively. So D is at position 3 and F is at position 4 (33 bags).
- The remaining person, B, sits at position 1.

The row arrangement from left to right is: B (Pos 1), E (Pos 2), D (Pos 3), F (Pos 4), C (Pos 5), A (Pos 6).

Step 2: Calculate the Bag Counts

1. D's Bags: D has an even square number of bags not less than 15. The even square in the allowed range (15 to 60) is $4^2=16$ bags.
2. B's Bags: B has 20 bags more than D, so B has $16+20=36$ bags.
3. A's Bags: A has 18 bags less than B, so A has $36-18=18$ bags.
4. E's Bags: E sits two places away from B (at position 3, D) plus 15 bags: $16+15=31$ bags (which is a prime number).

Step 3: Calculate the Sum of Bags at Extreme Ends

The persons at the extreme ends are B (position 1) and A (position 6).

$\text{Sum}=\text{B's bags}+\text{A's bags}=36+18=54$

Thus, the correct answer is 54.