X, Y and Z together finish work in 16 (4/11) days.
Converting to improper fraction:
16114=1116×11+4
=11176+4
=11180 days
Work rate of (X + Y + Z) together:
Work rate =time taken1=180/111=18011 work per day
X and Y together take 20 days.
Work rate of (X + Y) together:
Work rate =201 work per day
Z's work rate alone is the difference between the combined rate and (X + Y)'s rate:
Z's work rate =18011−201
=18011−1809
=1802
=901 work per day
Z completes the full work in:
Time =1/901=90 days
For 60% of the work:
Time =90×0.6
=54 days
Therefore, Z alone will finish 60% of the work in 54 days.