Introduction:
In this problem, we are given a BCC structure of element A with guest atoms B present at the face centres. Our task is to determine the packing fraction of the solid without disturbing the unit cell dimension.

Solution:
To solve the problem, we need to follow the steps given below:

Step 1:
Determine the number of atoms in the unit cell of element A in BCC structure. For BCC, the number of atoms in the unit cell is 2.

Step 2:
Determine the size of the guest atoms B. The largest possible size of the guest atoms is such that they touch each other along the face diagonal of the cube, without disturbing the unit cell dimension. In other words, the size of guest atoms B should be equal to the length of the face diagonal of the cube, which is √2 times the length of the edge of the cube.

Step 3:
Determine the volume of the unit cell of element A. For a BCC structure, the volume of the unit cell can be calculated as:

V = a^3 / 2

where a is the length of the edge of the cube.

Step 4:
Determine the volume of the atoms in the unit cell of element A. For a BCC structure, each atom occupies 1/2 of the volume of the cube. Therefore, the volume of the atoms in the unit cell can be calculated as:

V_atom = 1/2 x V

Step 5:
Determine the volume of the guest atoms B. For a face-centred cubic structure, the guest atoms B occupy 1/2 of the volume of the cube. Therefore, the volume of the guest atoms can be calculated as:

V_guest = 1/2 x V

Step 6:
Determine the total volume occupied by the atoms and guest atoms in the unit cell. This can be calculated as:

V_total = V_atom + V_guest

Step 7:
Determine the packing fraction of the solid. This can be calculated as:

Packing fraction = V_total / V

where V is the volume of the unit cell of element A.

Conclusion:
In this way, we can determine the packing fraction of the solid with guest atoms B present at the face centres of a BCC structure of element A, without disturbing the unit cell dimension.