Pipe X can fill a cistern thrice as fast as another pipe Y and the pipe Y is thrice as fast as pipe Z. If X, Y and Z together fill the cistern in 10 minutes then the time taken by X to fill the cistern is -

Let,
The pipe Z alone takes A minutes to fill the tank.
Given that,
Y is thrice as fast as Z.
Then, Y takes A/3 minutes to fill the tank.
And, X is thrice as fast as Y.
X takes (A/3)/3 = A/9 minutes to fill the tank.
Now,
Part filled by X in 1 minute = 9/A
Part filled by Y in 1 minute = 3/A
Part filled by Z in 1 minute = 1/A
Net part filled by (X+Y+Z) in 1 minute = 9/A + 3/A + 1/A
= 13/A
(X+Y+Z) take 10 minutes to fill the cistern.
Part filled by (X+Y+Z) in 1 minute = 1/10
Thus,
We have,
1/10 = 13/A
⇒ A = 13 × 10
⇒ A = 130
Therefore, Z alone takes 130 minutes
So, X can fill the cistern in 130/9 minutes.
Hence, the correct answer is - ঘ) none of these