40 men took a dip in a pool 30 metre long and 25 metre broad. If the average water displaced by a man is 5 `"metre"^(3)`, what will be the rise (in cm) in the water level of the pool ?

Options

A. a) 25
B. b) 26.66
C. c) 27.33
D. d) 28

Answer

To solve the problem of how much the water level in the pool will rise when 40 men take a dip, we can follow these steps:

### Step 1: Calculate the total volume of water displaced by the men.
Each man displaces an average of 5 cubic meters of water. Therefore, for 40 men, the total volume displaced can be calculated as:
\[ \text{Total Volume Displaced} = \text{Number of Men} \times \text{Volume Displaced by One Man} \]
\[ \text{Total Volume Displaced} = 40 \times 5 = 200 \text{ cubic meters} \]

### Step 2: Calculate the base area of the pool.
The pool is rectangular in shape, and its area can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given that the length of the pool is 30 meters and the breadth is 25 meters:
\[ \text{Area} = 30 \times 25 = 750 \text{ square meters} \]

### Step 3: Calculate the rise in water level.
To find the rise in water level (height), we can use the formula relating volume, area, and height:
\[ \text{Volume} = \text{Area} \times \text{Height} \]
Rearranging this formula to find height gives us:
\[ \text{Height} = \frac{\text{Volume}}{\text{Area}} \]
Substituting the values we have:
\[ \text{Height} = \frac{200}{750} \text{ meters} \]

### Step 4: Convert the height from meters to centimeters.
Since 1 meter = 100 centimeters, we convert the height:
\[ \text{Height in cm} = \frac{200}{750} \times 100 \]
Calculating this gives:
\[ \text{Height in cm} = \frac{20000}{750} \approx 26.67 \text{ cm} \]

### Final Answer:
The rise in the water level of the pool will be approximately **26.67 cm**.

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