A lamp post has half of its length in mud, `1/3` of its length in water and `3 1/3` m above the water. Find the total length of the post?

Options

A. 20m
B. 15m
C. 25m
D. 30m

Answer

To find the total length of the lamp post, we can break down the problem step by step:

### Step 1: Define the Variables
Let the total length of the lamp post be \( L \).

### Step 2: Express the Lengths in Terms of \( L \)
According to the problem:
- Half of the length is in mud: \( \frac{1}{2}L \)
- One third of the length is in water: \( \frac{1}{3}L \)
- The remaining part is above water, which is given as \( 3 \frac{1}{3} \) meters.

### Step 3: Convert Mixed Number to Improper Fraction
Convert \( 3 \frac{1}{3} \) to an improper fraction:
\[ 3 \frac{1}{3} = \frac{10}{3} \text{ meters} \]

### Step 4: Set Up the Equation
The total length of the lamp post can be expressed as:
\[ \frac{1}{2}L + \frac{1}{3}L + \frac{10}{3} = L \]

### Step 5: Combine the Fractions
To combine \( \frac{1}{2}L \) and \( \frac{1}{3}L \), we need a common denominator. The least common multiple of 2 and 3 is 6.
- Convert \( \frac{1}{2}L \) to sixths:
\[ \frac{1}{2}L = \frac{3}{6}L \]
- Convert \( \frac{1}{3}L \) to sixths:
\[ \frac{1}{3}L = \frac{2}{6}L \]

Now, we can combine them:
\[ \frac{3}{6}L + \frac{2}{6}L = \frac{5}{6}L \]

### Step 6: Substitute Back into the Equation
Substituting back into the equation gives:
\[ \frac{5}{6}L + \frac{10}{3} = L \]

### Step 7: Isolate \( L \)
To isolate \( L \), subtract \( \frac{5}{6}L \) from both sides:
\[ \frac{10}{3} = L - \frac{5}{6}L \]
This simplifies to:
\[ \frac{10}{3} = \frac{1}{6}L \]

### Step 8: Solve for \( L \)
To find \( L \), multiply both sides by 6:
\[ L = 6 \times \frac{10}{3} = 20 \text{ meters} \]

### Conclusion
The total length of the lamp post is \( 20 \) meters.

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