One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part above the water is greater than or equal to 3 metres . Find the length of the shortest pole.

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Solution

Let length of bamboo pole = x m
So,
So part buried in mud $= \frac{x}{3}$
And
Part buried In water $= \frac{x}{6}$
Total length of pole that is buried in mud and water $= \frac{x}{3} + \frac{x}{6} = \frac{2 x + x}{6} = \frac{x}{2},$
Now as given part is above water is greater than or equal to 3 m, and we want to find smallest length of that pole, so we take it as 3m.

$x - \frac{x}{2} = 3$
On solving, we get
x = 6 m This is the shortest length of our bamboo pole, or if we take part above the water is greater than 3, than we get our length of pole is more than 6 m.
So,
Shortest length of the pole = 6 m

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