0.1 and $$\frac{5}{8}$$ of a bamboo are in mud and water respectively and rest length 2.75 m is above water. What is length of bamboo ?

$${\text{0}}{\text{.1 = }}\frac{1}{{10}}\left( {{\text{mud}}} \right),\,\,\,\,\frac{5}{8}\left( {{\text{water}}} \right)$$
Let total length of bamboo = 40x ( LCM of 8, 10 )
$$\eqalign{ & {\text{Mud part :}} \cr & {\text{ = }}\frac{1}{{10}} \times 40x = 4x \cr & {\text{Water part :}} \cr & {\text{ = }}\frac{5}{8} \times 40x = 25x \cr & {\text{Remaining part :}} \cr & = (40x - 25x - 4x) \cr & = 11x \cr & 11x{\text{ }} \to {\text{ }}2.75m \cr & {\text{ }}x{\text{ }} \to {\text{ }}0.25m \cr & 40x{\text{ }} \to {\text{ }}10m \cr} $$