correct answer is: c) 30 meters

Explanation

Let, the length of the bamboo be ‘x’ .
According to the question,
\large\frac{1}{3} ^rd part of the length of a bamboo is coloured red.
\therefore Red coloured length =\large\left(\frac{1}{3}\times\normalsize x\right) m
\rightarrow\large\frac{x}{3} m.

\large\frac{1}{5} ^th part of the length of a bamboo is coloured green.
\therefore Green coloured length =\large\left(\frac{1}{5}\times\normalsize x\right) m
\rightarrow\large\frac{x}{5} m.

Remaining 14 m length is coloured yellow.

In line with the inquiry,
\large\left(\frac{x}{3}+\frac{x}{5}+\normalsize14\right)=x
\rightarrow\large\left(\frac{5x+3x+210}{15}\right)=x _{[L.C.M = 15]}
\rightarrow15x=8x+210 _{[interchange]}
\rightarrow15x-8x=210
\rightarrow7x=210
\rightarrow x=\large\frac{210}{7}
\rightarrow x=30 m
\therefore The length of the bamboo is 30 m.
Ans: The length of the bamboo is 30 meters.

Additional variations of this particular query are:
1. Find the total length of a bamboo given that 1/3rd is colored red, 1/5th is colored green, and the remaining 14 meters is colored yellow.
2. Determine the length of the bamboo if 1/3rd is painted red, 1/5th is painted green, and the rest is painted yellow, with a total length of 14 meters.
3. Calculate the length of the bamboo when fractions of 1/3rd and 1/5th are painted red and green respectively, and the remaining length is yellow, totaling 14 meters.
4. What is the total length of the bamboo if 1/3rd is colored red, 1/5th is colored green, and the remaining part is colored yellow, totaling 14 meters?
5. Find the length of the bamboo given that fractions of 1/3rd and 1/5th are painted red and green respectively, and the remaining 14 meters is colored yellow.