Forty men take a dip in a rectangular swimming pool 30 m long and 25 m broad. If each man displaces on average 5 cubic metres of water, by how many centimetres will the water level in the pool rise?

Introduction / Context:
This is a practical volume and level rise question related to a swimming pool. When people enter the pool, they displace water, and the level of water rises. The problem assesses understanding of volume conservation: the total volume displaced must equal the increase in volume of water in the pool. It combines basic mensuration of a cuboid with unit conversion from metres to centimetres.

Given Data / Assumptions:

- The swimming pool is rectangular with length 30 m and breadth 25 m.
- Forty men enter the pool and each displaces 5 cubic metres of water on average.
- Total displaced volume is the sum of the volumes displaced by all men.
- The water spreads uniformly over the entire base area of the pool, raising the water level by the same amount everywhere.
- We need to find the rise in water level in centimetres.

Concept / Approach:
The volume increase in a pool is given by rise in water level multiplied by the base area of the pool. The total volume of water displaced by the men becomes this volume increase. Therefore, rise in height h can be computed as total displaced volume V divided by the base area A. After finding h in metres, we convert it to centimetres by multiplying by 100.

Step-by-Step Solution:
Step 1: Base area of the pool A = length * breadth = 30 * 25 = 750 square metres.Step 2: Each man displaces 5 cubic metres of water.Step 3: Total number of men = 40. Total volume displaced V = 40 * 5 = 200 cubic metres.Step 4: Let the rise in water level be h metres.Step 5: Volume increase in the pool = base area * rise in height = A * h = 750 * h.Step 6: This volume must equal the displaced volume, so 750 * h = 200.Step 7: Therefore, h = 200 / 750 = 2 / 7.5 = 0.2666 recurring, which is approximately 0.2667 metres or 26.67 centimetres.

Verification / Alternative check:
You can double check the conversion: 0.2667 m multiplied by 100 equals 26.67 cm. Also, if the pool had area 100 square metres instead, the same volume would raise the level by 2 metres. Since our pool has a much larger area of 750 square metres, the rise must be much smaller than 2 metres, so a value around 0.27 metres is quite reasonable.

Why Other Options Are Wrong:
25.0 cm and 27.33 cm are close but not equal to the precise computed value and usually result from rounding mistakes or approximating the fraction 200 / 750 incorrectly. 28.5 cm and 30.0 cm overestimate the rise and would require a smaller base area or a larger displaced volume. Only 26.67 cm matches the exact calculation based on given data.

Common Pitfalls:
A common error is to use the pool perimeter instead of its area when relating volume to level rise. Another mistake is to forget to convert the final height from metres to centimetres, leaving the answer as 0.2667 instead of 26.67 cm. Some learners also miscalculate the total displaced volume or mis-handle fractions when dividing 200 by 750. Careful use of units and arithmetic avoids these issues.

Final Answer:
The water level in the pool rises by approximately 26.67 cm.