On a certain religious day, 50 men take a dip in a rectangular water tank that is 40 m long and 20 m broad. If each man displaces an average of 4 cubic metres of water, by how much will the water level in the tank rise, in centimetres?

Introduction / Context:
This question involves the principle that when bodies are immersed in water, they displace water equal to their own volume. The displaced water causes the water level in the container to rise. Here, a group of men are taking a dip in a rectangular tank, and each man displaces a known volume of water. We must compute how much the water level rises. This problem is a straightforward application of volume conservation and the formula for the volume of a rectangular prism.

Given Data / Assumptions:

• Number of men = 50.
• Average volume of water displaced by each man = 4 cubic metres.
• Tank length L = 40 m.
• Tank breadth B = 20 m.
• Rise in water level is uniform across the tank.

Concept / Approach:
Total volume of water displaced by all men equals the volume corresponding to the rise in water level in the tank. For a rectangular tank, volume increase due to rise in level h is:
Volume rise = L * B * h Total displaced volume V disp is:
V disp = number of men * volume displaced per man Equating these volumes gives L * B * h = V disp, from which we solve for h. Finally, we convert h from metres to centimetres.

Step-by-Step Solution:
Step 1: Compute total displaced volume. V disp = 50 * 4 = 200 cubic metres. Step 2: Express volume rise in terms of h. Volume rise = L * B * h = 40 * 20 * h. Volume rise = 800 * h cubic metres. Step 3: Equate displaced volume with volume rise. 800 * h = 200. h = 200 / 800 = 1 / 4 metre. Step 4: Convert h to centimetres. h = 1 / 4 metre = 0.25 metre. 0.25 metre = 0.25 * 100 = 25 centimetres. So, the water level rises by 25 centimetres.

Verification / Alternative check:
We can check that 25 cm is reasonable. The base area of the tank is 40 * 20 = 800 square metres. Multiplying this by a rise of 0.25 metre gives a volume of 800 * 0.25 = 200 cubic metres, which equals the total displaced volume. Thus the calculation is consistent.

Why Other Options Are Wrong:
Option A (20 cm) would correspond to a rise of 0.20 metre, which would only add 160 cubic metres of water, less than the displaced 200 cubic metres. Option C (35 cm) and Option D (50 cm) correspond to rises that would yield volumes larger than 200 cubic metres. Option E (10 cm) is much too small and would increase the volume by only 80 cubic metres.

Common Pitfalls:
The most common mistakes are forgetting to convert metres to centimetres or miscalculating the total displaced volume by mistakenly multiplying by 10 or missing a zero. Another error is to assume the tank is square instead of rectangular, using the wrong base area. Always compute the total displaced volume first, then divide by the correct base area to find the height of the water rise.

Final Answer:
The water level in the tank will rise by 25 centimetres.