Water flows into a rectangular tank that is 200 m long and 150 m wide through a pipe of cross section 0.3 m x 0.2 m at a speed of 20 km/h. In how many hours will the water level in the tank rise by 12 m?

Introduction / Context:
This question tests the standard pipes and cistern idea that time taken to fill a container equals volume divided by flow rate. Here the tank is large and water is flowing through a pipe with a given cross section and speed, so we must convert the speed into consistent units and then compute the time required for the water level to rise by a fixed height of 12 m.

Given Data / Assumptions:
- Length of tank = 200 m
- Width of tank = 150 m
- Rise in water level required = 12 m
- Pipe cross section = 0.3 m x 0.2 m
- Flow speed in pipe = 20 km per hour = 20000 m per hour
- Assume uniform flow and no leakage or spillage

Concept / Approach:
The key ideas are:
- Volume of water required = base area of tank * rise in level
- Discharge (flow rate) of pipe = cross sectional area of pipe * velocity of water in the pipe
- Time = required volume / flow rate, with all quantities in consistent units (here in cubic metres and hours).

Step-by-Step Solution:
Step 1: Base area of tank = length * width = 200 * 150 = 30000 m^2. Step 2: Volume needed for 12 m rise = 30000 * 12 = 360000 m^3. Step 3: Cross sectional area of pipe = 0.3 * 0.2 = 0.06 m^2. Step 4: Convert speed: 20 km/h = 20000 m/h. Step 5: Flow rate of pipe = 0.06 * 20000 = 1200 m^3 per hour. Step 6: Time required = volume / rate = 360000 / 1200 = 300 hours.

Verification / Alternative check:
We can simplify the fraction 360000 / 1200 by dividing numerator and denominator by 100 to get 3600 / 12 = 300. Units also check out as hours since we used m^3 and m^3 per hour. The magnitude is large because the tank is extremely big compared with the relatively small pipe.

Why Other Options Are Wrong:
200 hours: This is too small and would correspond to a higher flow rate than given by the pipe dimensions and speed.
240 hours: Also underestimates the required time because it assumes either a smaller volume or a larger discharge than the actual values.
270 hours: Slightly closer but still not equal to the exact ratio 360000 / 1200, so it is not correct.

Common Pitfalls:
A frequent mistake is to forget to convert 20 km/h into metres per hour, or to mix hours and minutes. Another error is to treat 12 m as the total depth instead of the rise in level, although here both interpretations match because the initial level is not specified. Always ensure that area, velocity and volume are in compatible units before computing time.

Final Answer:
The required time for the water level in the tank to rise by 12 m is 300 hours.