A field is 120 m. long and 50 m broad. A tank 24 m long. 10 m broad and 6 m deep is dug any where in the field and the earth taken out of the tank is evenly spread over the remaining part of the field . Find the rise in level of the field.

Answer

To solve the problem step by step, we will follow the logical sequence of calculations as described in the video transcript.

### Step 1: Calculate the area of the field
The area of the field can be calculated using the formula for the area of a rectangle, which is:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length of the field = 120 m
- Breadth of the field = 50 m

Calculating the area:
\[ \text{Area of the field} = 120 \, \text{m} \times 50 \, \text{m} = 6000 \, \text{m}^2 \]

### Step 2: Calculate the area of the tank
The area of the tank can also be calculated using the same formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length of the tank = 24 m
- Breadth of the tank = 10 m

Calculating the area:
\[ \text{Area of the tank} = 24 \, \text{m} \times 10 \, \text{m} = 240 \, \text{m}^2 \]

### Step 3: Calculate the remaining area of the field
To find the remaining area of the field after the tank has been dug, we subtract the area of the tank from the area of the field:
\[ \text{Remaining Area} = \text{Area of the field} - \text{Area of the tank} \]
Calculating the remaining area:
\[ \text{Remaining Area} = 6000 \, \text{m}^2 - 240 \, \text{m}^2 = 5760 \, \text{m}^2 \]

### Step 4: Calculate the volume of earth dug out from the tank
The volume of the tank can be calculated using the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Depth} \]
Given:
- Depth of the tank = 6 m

Calculating the volume:
\[ \text{Volume of the tank} = 24 \, \text{m} \times 10 \, \text{m} \times 6 \, \text{m} = 1440 \, \text{m}^3 \]

### Step 5: Calculate the rise in level of the field
The volume of earth dug out will be spread evenly over the remaining area of the field. We can set up the equation:
\[ \text{Volume dug} = \text{Remaining Area} \times \text{Rise in level} \]
Let \( h \) be the rise in level. Therefore:
\[ 1440 \, \text{m}^3 = 5760 \, \text{m}^2 \times h \]

Now, solving for \( h \):
\[ h = \frac{1440 \, \text{m}^3}{5760 \, \text{m}^2} = \frac{1}{4} \, \text{m} = 0.25 \, \text{m} \]

### Final Answer:
The rise in the level of the field is **0.25 meters**.

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