You've found out for 1 hour's work and you need to find out for the full work.

Note that Yand Z together should take less time than X. Therefore their ratio should be smaller.

Hi Nisha,
The Q asks us to find ratio of time take and not rate, in your explanation you have taken ratios of their rates thats why u got the reciprocal of the ans

now time for machine x is 12 hrs

y & z combined i.e combine their rates so we have 1/15 +1/18

i.e 33/15X18
i.e 11/90
we know that R X t =w
hence combined time of y & z is 1/(11/90) i.e 90/11

so our ratio is 12/90/11 i.e 12X11/90

i.e 22/15

In such q's you can always double check the numerator & denominator of the fraction you get as the answer& ask your self a question that which one should be bigger.