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

Options

A. 25
B. `26.66`
C. `27.33`
D. `28`

Answer

To solve the problem step by step, we will follow these calculations:

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

### Step 2: Calculate the volume of the pool.
The volume of the pool can be calculated using the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]
We know the length and breadth of the pool:
- Length = 30 meters
- Breadth = 25 meters

Let \( h \) be the rise in water level (height) in meters. Thus, the volume of the pool due to the rise in water level is:
\[ \text{Volume} = 30 \times 25 \times h \]

### Step 3: Set the volume of water displaced equal to the volume of the pool.
Since the volume of water displaced is equal to the volume of the rise in the pool, we can set up the equation:
\[ 200 = 30 \times 25 \times h \]

### Step 4: Solve for \( h \).
Rearranging the equation to solve for \( h \):
\[ h = \frac{200}{30 \times 25} \]
Calculating the denominator:
\[ 30 \times 25 = 750 \]
Now substituting back:
\[ h = \frac{200}{750} = \frac{4}{15} \text{ meters} \]

### Step 5: Convert \( h \) from meters to centimeters.
Since 1 meter = 100 centimeters, we convert \( h \):
\[ h = \frac{4}{15} \times 100 = \frac{400}{15} \text{ centimeters} \]
Now simplifying:
\[ \frac{400}{15} \approx 26.67 \text{ centimeters} \]

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

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