Seven boxes B, C, D, P, Q, R and S are kept one over the other but not necessarily in the same order. Only three boxes are kept above B. Only one box is kept between P and B. Only three boxes are kept between P and R. R is kept at some place above B. D is kept immediately below R. Q is kept at one of the places above S. C is not kept immediately above or below P.

Which box is kept at the lowermost position?

The correct option is S.

Let us determine the step-by-step arrangement of the seven boxes (B, C, D, P, Q, R, and S) from top to bottom (positions 1 to 7, where 1 is the topmost and 7 is the lowermost position):

Step 1: Position of Box B
According to the clue, "Only three boxes are kept above B." This means B must be placed at the 4th position from the top.
Positions layout so far:
1. [Empty]
2. [Empty]
3. [Empty]
4. B
5. [Empty]
6. [Empty]
7. [Empty]

Step 2: Position of Box P
"Only one box is kept between P and B." This gives two possibilities for P:
- Case 1: P is at position 2 (above B).
- Case 2: P is at position 6 (below B).

Step 3: Position of Box R
"Only three boxes are kept between P and R." Let us evaluate this for both cases:
- Under Case 1 (P at position 2): R must be placed at position 6 (leaving positions 3, 4, and 5 between them). But we are also told "R is kept at some place above B." Since B is at position 4 and position 6 is below position 4, this violates the condition. Thus, Case 1 is eliminated.
- Under Case 2 (P at position 6): R must be placed at position 2 (leaving positions 3, 4, and 5 between them). In this scenario, R (at position 2) is indeed kept at a place above B (at position 4). This arrangement is valid.
Positions layout so far:
1. [Empty]
2. R
3. [Empty]
4. B
5. [Empty]
6. P
7. [Empty]

Step 4: Position of Box D
"D is kept immediately below R." Since R is at position 2, D must be at position 3.
Positions layout so far:
1. [Empty]
2. R
3. D
4. B
5. [Empty]
6. P
7. [Empty]

Step 5: Position of Box C
"C is not kept immediately above or below P." The remaining empty positions are 1, 5, and 7.
- Position 5 is immediately above P (at position 6).
- Position 7 is immediately below P (at position 6).
Therefore, C cannot be at position 5 or 7. This forces C to be placed at position 1.
Positions layout so far:
1. C
2. R
3. D
4. B
5. [Empty]
6. P
7. [Empty]

Step 6: Positions of Q and S
The remaining empty positions are 5 and 7. We are given that "Q is kept at one of the places above S."
Thus, Q must be placed at position 5, and S must be placed at position 7.
The final arrangement of the boxes from top to bottom is:
1. C
2. R
3. D
4. B
5. Q
6. P
7. S

Therefore, box S is kept at the lowermost position (position 7).