Solution:

Given:
Focal length of objective lens (f1) = 1 cm
Focal length of eye lens (f2) = 5 cm
Magnifying power for relaxed eye (M) = 45

We know that the formula for the magnifying power of a compound microscope is given by:
M = (1 + D) x (1 + d)
Where D is the angular magnification produced by the objective lens and d is the angular magnification produced by the eye lens.

To find the length of the tube, we need to calculate the angular magnifications produced by the objective and eye lens.

Finding the angular magnification produced by the objective lens:
The angular magnification produced by the objective lens can be calculated using the formula:
D = (25 cm) / (f1)
Here, the distance between the object and the objective lens (d1) is considered as 25 cm because the final image formed by the microscope is at least at the least distance of distinct vision (25 cm).

Substituting the given values, we get:
D = (25 cm) / (1 cm) = 25

Finding the angular magnification produced by the eye lens:
The angular magnification produced by the eye lens can be calculated using the formula:
d = (D) / (M)
Here, the angular magnification produced by the objective lens (D) and the magnifying power (M) are given.

Substituting the given values, we get:
d = (25) / (45) = 5/9

Calculating the length of the tube:
The total angular magnification of the microscope is given by:
M = (1 + D) x (1 + d)

Substituting the values of D and d that we calculated earlier, we get:
45 = (1 + 25) x (1 + 5/9)

Simplifying the equation, we get:
45 = (26) x (14/9)

Solving for the length of the tube, we get:
Length of the tube = (45 x 9) / (26 x 14) = 15 cm

Therefore, the length of the tube is 15 cm.
Hence, the correct option is (c) 15 cm.