X can do a certain work in 84 days. Y in 50% less efficient than X while Z takes 28 days to do the same work. To complete the work, Y started the work, X joined him after 3 days and Z joined them after 7 days from the beginning. For how many days did Z work to complete the work?

1 Day work of X = 1/84 th part of work 1 Day work of Y = 1 /168th part of work 1 Day work of Z = 1/28 the part of work 1 1 Day work of X and Y together =1/84 + 1/168 = 1/56 th part of work 1 Day work of X, Y and Z 1 together = 1/84 +1/168 +1/28= 3/56th part of work For 3 days, Y worked alone and completed = 3 x 1/168 =1/56th part of work  1 For next 4 days, X and Y worked together and completed = 4 ×1/56 =1/14 the part of work  Now, remaining work after 7 days