Introduction:
In this problem, we are given a rectangular timber beam that is simply supported at the ends and carries a concentrated load at mid-span. We are also given the maximum bending stress and maximum shear stress in the beam. We need to find the ratio of span to depth of the beam.

Formula:
The formula for maximum bending stress in a rectangular beam is given by:

σ = (M*y) / I

where,
σ = maximum bending stress
M = maximum bending moment
y = distance from the neutral axis to the point where maximum bending stress occurs
I = moment of inertia of the cross-section of the beam

The formula for maximum shear stress in a rectangular beam is given by:

τ = (V*Q) / (I*t)

where,
τ = maximum shear stress
V = maximum shear force
Q = first moment of area
I = moment of inertia of the cross-section of the beam
t = thickness of the beam

Solution:
We are given that the maximum bending stress in the beam is 12N/mm^2 and the maximum shear stress is 1.2N/mm^2.

Step 1: Finding the ratio of maximum bending moment to maximum shear force

From the given data, we can write:

Maximum bending stress = (M*y) / I

Maximum shear stress = (V*Q) / (I*t)

Dividing the two equations, we get:

(M*y) / (V*Q) = maximum bending stress / maximum shear stress = 12 / 1.2 = 10

Therefore, the ratio of maximum bending moment to maximum shear force is 10.

Step 2: Finding the ratio of span to depth

For a rectangular beam, the maximum bending moment occurs at mid-span and is given by:

M = (w*l^2) / 8

where,
w = load on the beam
l = span of the beam

The maximum shear force at mid-span is given by:

V = w / 2

The first moment of area of the cross-section of the beam about the neutral axis is given by:

Q = (b*h^2) / 12

where,
b = width of the beam
h = depth of the beam

The moment of inertia of the cross-section of the beam is given by:

I = (b*h^3) / 12

Substituting the values in the formula for maximum shear stress, we get:

1.2 = (w*l*b*h/2) / ((b*h^2/12)*(h/2))

Simplifying the above equation, we get:

l/h = 1.5

Substituting the value of l/h in the formula for maximum bending moment, we get:

M = (w*h^2) / 4

Substituting the value of M and V in the formula for the ratio of maximum bending moment to maximum shear force, we get:

(wh^2/4) / (w*h/2 * b*h^2/12) = 10

Simplifying the above equation, we get:

l/h = 16

Therefore, the ratio of span to depth of the beam is 16.

Conclusion:
The ratio of span to depth of the rectangular timber beam is 16.