`4/7` of a pole is in the mud. When `1/3` of it is pulled out, an 8 m long piece of the pole still remains in the mud. What is the total length of the pole?

Options

A. 21 m
B. 25 m
C. 30 m
D. 12 m

Answer

To solve the problem step by step, we can follow the reasoning outlined in the video transcript:

### Step 1: Define the total length of the pole
Let the total length of the pole be represented as \( L \). According to the problem, we can express this length in terms of a variable \( x \):
\[ L = 7x \]

### Step 2: Determine the length of the pole in the mud
We know that \( \frac{4}{7} \) of the pole is in the mud. Therefore, the length of the pole that is in the mud can be calculated as:
\[ \text{Length in mud} = \frac{4}{7}L = \frac{4}{7}(7x) = 4x \]

### Step 3: Calculate the length of the pole pulled out
When \( \frac{1}{3} \) of the pole in the mud is pulled out, we can find out how much is pulled out:
\[ \text{Length pulled out} = \frac{1}{3}(4x) = \frac{4x}{3} \]

### Step 4: Determine the remaining length in the mud
After pulling out \( \frac{1}{3} \) of the pole in the mud, the remaining length in the mud is:
\[ \text{Remaining in mud} = 4x - \frac{4x}{3} \]
To simplify this, we can find a common denominator:
\[ \text{Remaining in mud} = \frac{12x}{3} - \frac{4x}{3} = \frac{8x}{3} \]

### Step 5: Set up the equation based on the problem statement
According to the problem, the remaining length in the mud is also given as 8 meters:
\[ \frac{8x}{3} = 8 \]

### Step 6: Solve for \( x \)
To find \( x \), we can multiply both sides of the equation by 3:
\[ 8x = 24 \]
Now, divide both sides by 8:
\[ x = 3 \]

### Step 7: Calculate the total length of the pole
Now that we have the value of \( x \), we can find the total length of the pole:
\[ L = 7x = 7 \times 3 = 21 \text{ meters} \]

### Final Answer
The total length of the pole is \( 21 \) meters.

---