`4//7` of a pole in the mud. When `1//3` of it is pulled out, 250 cm of the pole is still in the mud. Find the full length of the pole.

Options

A. 1000
B. 1100
C. 950
D. 1050

Answer

To solve the problem step by step, let's denote the full length of the pole as \( L \).

### Step 1: Understand the fractions involved
According to the problem, \( \frac{4}{7} \) of the pole is in the mud. This means that the length of the pole that is in the mud is \( \frac{4}{7}L \).

### Step 2: Determine the length of the pole pulled out
When \( \frac{1}{3} \) of the pole is pulled out, the length pulled out is:
\[ \text{Length pulled out} = \frac{1}{3}L \]

### Step 3: Calculate the remaining length in the mud
After pulling out \( \frac{1}{3}L \), the remaining length of the pole in the mud can be calculated as:
\[ \text{Remaining length in mud} = \frac{4}{7}L - \frac{1}{3}L \]

### Step 4: Find a common denominator
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 7 and 3 is 21. We can rewrite the fractions:
\[ \frac{4}{7}L = \frac{12}{21}L \quad \text{and} \quad \frac{1}{3}L = \frac{7}{21}L \]

### Step 5: Perform the subtraction
Now we can subtract:
\[ \text{Remaining length in mud} = \frac{12}{21}L - \frac{7}{21}L = \frac{5}{21}L \]

### Step 6: Set up the equation
According to the problem, the remaining length in the mud is equal to 250 cm:
\[ \frac{5}{21}L = 250 \]

### Step 7: Solve for \( L \)
To find \( L \), we can multiply both sides by \( \frac{21}{5} \):
\[ L = 250 \times \frac{21}{5} \]

### Step 8: Calculate \( L \)
Now, calculate:
\[ L = 250 \times 4.2 = 1050 \text{ cm} \]

### Conclusion
The full length of the pole is \( 1050 \) cm.

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