Given information:
- The house-top water tank is made of flat plates.
- The tank is full to the brim.
- The height of the tank is twice that of any side.

To find:
The ratio of total thrust force on the bottom of the tank to that on any side.

Solution:
1. Understanding the concept of thrust force:
Thrust force is the force exerted by a fluid (in this case, water) on a surface due to the pressure exerted by the fluid. The thrust force is always perpendicular to the surface.

2. Analysis of the tank:
Since the tank is full to the brim, the water exerts pressure on all the surfaces of the tank, including the bottom and the sides. Let's consider a rectangular tank for easier analysis.

3. Thrust force on the bottom of the tank:
The thrust force on the bottom of the tank is equal to the pressure exerted by the water multiplied by the area of the bottom surface. Since the tank is full to the brim, the pressure at the bottom is the same as the pressure at any other point inside the tank. Therefore, the thrust force on the bottom is equal to the pressure multiplied by the area of the bottom surface.

4. Thrust force on any side of the tank:
The thrust force on any side of the tank is equal to the pressure exerted by the water multiplied by the area of that side. The pressure at any point on the side is equal to the pressure at the same height inside the tank. Therefore, the thrust force on any side is equal to the pressure multiplied by the area of that side.

5. Comparison of thrust forces:
Let's assume the length of the tank is L, the width is W, and the height is H. According to the given information, H = 2W.

- Thrust force on the bottom: Pressure x Area of bottom = Pressure x (L x W)
- Thrust force on any side: Pressure x Area of side = Pressure x (L x H)

Since H = 2W, the thrust force on any side becomes Pressure x (L x 2W) = Pressure x (2LW) = 2 x (Pressure x LW)

6. Ratio of thrust forces:
The ratio of total thrust force on the bottom of the tank to that on any side can be calculated as follows:

Total thrust force on the bottom / Thrust force on any side = (Pressure x (L x W)) / (2 x (Pressure x LW))

The pressure cancels out, as it is the same for both cases. Similarly, the length (L) cancels out.

Therefore, the ratio simplifies to:

Total thrust force on the bottom / Thrust force on any side = W / (2W) = 1/2 = 0.5

Conclusion:
The ratio of the total thrust force on the bottom of the tank to that on any side is 0.5, which corresponds to option (B).