Problem Solving

Working alone, printers X,Y, Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?

A) 4/11
B) 1/2
C) 15/22
D) 22/15
E) 11/4

The answer is D.(I don't know how to use the spoiler to hide the answer. Please guide me)

I don't understand the part why x is 12/1 instead of 1/12? Can someone please explain it to me?

Thank you in advance.

X takes 12 hours to do 1 job
Y takes 15 hours to do 1 job
Z takes 18 hours to do 1 job

Therefore, X, Y and Z takes 1 hour to do 1/12, 1/15 and 1/18 jobs respectively.

By that logic,

Y and Z combined takes 1 hour to do (18+15)/18*15 job = 11/90 job.
But Y and Z combined take 90/11 hours to do 1 job.
Similarly X takes 12 hours to do 1 job.

Ratio of times - X:Y+Z
12:90/11

translates to 132/90 which simplifies to 22/15. Answer D.

Regards
Anup