In which of the following option, the first box is kept exactly in the middle of the second and third box?

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

Nine boxes – A, B, C, D, E, F, G, H and I are kept one above another in a single stack but not necessarily in the same order.

Only three boxes are kept between the boxes E and H. Only two boxes are kept between the boxes H and B. Box B is not kept adjacent to box E. Box I is kept two boxes below the box C. As many boxes are kept above the box I as below the box D. More than two boxes are kept between the boxes D and F. Box F is kept below the box C. Box G is kept above the box A but not kept on the topmost position.

To determine the correct option, let us first find the exact step-by-step arrangement of all nine boxes from top (position 9) to bottom (position 1).

Step 1: Analyze the given clues

1. Exactly 3 boxes are kept between E and H.
2. Exactly 2 boxes are kept between H and B.
3. Box B is not adjacent to box E.
4. Box I is kept two boxes below box C (i.e., Position of I = Position of C - 2).
5. The number of boxes kept above box I is equal to the number of boxes kept below box D.
6. More than 2 boxes are kept between D and F.
7. Box F is kept below box C.
8. Box G is kept above box A, but G is not on the topmost position (Position 9).

Step 2: Placing the boxes in the stack

From the clues, testing the valid relative positions yields the unique top-to-bottom order (from Position 9 down to Position 1):

Position 9 (Top): Box B
Position 8: Box G
Position 7: Box D
Position 6: Box H
Position 5: Box C
Position 4: Box A
Position 3: Box I
Position 2: Box E
Position 1 (Bottom): Box F

Step 3: Verification of the correct option

We need to check the option AHE where the first box (A) is kept exactly in the middle of the second box (H) and the third box (E):

$\text{Position of Box H}=6$
$\text{Position of Box E}=2$
$\text{Midpoint Position}=\frac{6+2}{2}=4$

Since Box A is located at Position 4, it is kept exactly in the middle of Box H and Box E.

The correct answer is AHE.