Question:
There is a pole in a lake, one half of the pole is buried in soil, another one third is submerged in water, and 2 meters are out of the water. What is the total length of the pole?
There is a pole in a lake, one half of the pole is buried in soil, another one third is submerged in water, and 2 meters are out of the water. What is the total length of the pole?
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When dealing with problems involving fractions of a total length, express each part as a fraction and set up an equation to solve for the total.
Updated On: Jan 9, 2026
- 10 meters
- 12 meters
- 14 meters
- 18 meters
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The Correct Option is B
Solution and Explanation
Step 1: Setting up the equation.
Let the total length of the pole be \( L \). We are told that: - Half of the pole is buried in the soil, so \( \frac{L}{2} \) is buried. - One third of the pole is submerged in water, so \( \frac{L}{3} \) is submerged. - 2 meters of the pole are out of the water. Thus, the total length \( L \) satisfies the equation: \[ \frac{L}{2} + \frac{L}{3} + 2 = L. \]
Step 2: Solving the equation.
First, find a common denominator: \[ \frac{3L}{6} + \frac{2L}{6} + 2 = L \implies \frac{5L}{6} + 2 = L. \] Subtract \( \frac{5L}{6} \) from both sides: \[ 2 = L - \frac{5L}{6} \implies 2 = \frac{L}{6}. \] Multiply both sides by 6: \[ L = 12. \]
Step 3: Conclusion.
Thus, the total length of the pole is (B) 12 meters.
Let the total length of the pole be \( L \). We are told that: - Half of the pole is buried in the soil, so \( \frac{L}{2} \) is buried. - One third of the pole is submerged in water, so \( \frac{L}{3} \) is submerged. - 2 meters of the pole are out of the water. Thus, the total length \( L \) satisfies the equation: \[ \frac{L}{2} + \frac{L}{3} + 2 = L. \]
Step 2: Solving the equation.
First, find a common denominator: \[ \frac{3L}{6} + \frac{2L}{6} + 2 = L \implies \frac{5L}{6} + 2 = L. \] Subtract \( \frac{5L}{6} \) from both sides: \[ 2 = L - \frac{5L}{6} \implies 2 = \frac{L}{6}. \] Multiply both sides by 6: \[ L = 12. \]
Step 3: Conclusion.
Thus, the total length of the pole is (B) 12 meters.
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