To find the ratio of power transmitted by the two shafts, we need to consider the relationship between power, torque, and angular velocity. The power transmitted by a shaft can be calculated using the formula:

P = T * ω

Where P is the power, T is the torque, and ω is the angular velocity.

The torque transmitted by a shaft can be calculated using the formula:

T = (π/16) * d^3 * τ

Where T is the torque, d is the diameter of the shaft, and τ is the shear stress.

Let's consider the solid shaft first:

Given: Diameter of solid shaft = 200 mm

The cross-sectional area of the solid shaft can be calculated using the formula:

A = π * (d^2)/4

Where A is the cross-sectional area and d is the diameter of the shaft.

Substituting the given diameter, we get:

A = π * (200^2)/4 = 31416 mm^2

Now let's consider the hollow shaft:

Given: Inside diameter of hollow shaft = 150 mm

The cross-sectional area of the hollow shaft can be calculated using the same formula as above:

A = π * (d^2)/4

Substituting the given inside diameter, we get:

A = π * (150^2)/4 = 17671 mm^2

The ratio of the cross-sectional areas of the two shafts can be calculated as:

Ratio = A_solid / A_hollow = 31416 / 17671 = 1.7777...

Now, since the two shafts have the same material, the shear stress can be assumed to be the same for both shafts. Therefore, the torque transmitted by the two shafts can be compared using the formula:

T_solid / T_hollow = (d_solid^3) / (d_hollow^3)

Substituting the given diameters, we get:

T_solid / T_hollow = (200^3) / (150^3) = 8/3 = 2.666...

Finally, to find the ratio of power transmitted by the two shafts, we can substitute the torque ratio into the power formula:

P_solid / P_hollow = (T_solid * ω) / (T_hollow * ω)

Since the angular velocity is the same for both shafts, it cancels out:

P_solid / P_hollow = T_solid / T_hollow = 2.666...

Rounded to one decimal place, the ratio of power transmitted by the two shafts is approximately 1.7, which corresponds to option C.