X, Y and Z can do a piece of work in 46 days, 92 days and 23 days, respectively. X started the work. Y joined him after 2 days. If Z joined them after 8 days from the beginning, then for how many days did X work?

18

X = 46 days, Y = 92 days, Z = 23 days,

⇒ Here, X worked alone for 2 days ⇒ 2 x 2 = 4 units  ..(Efficiency × Days = Work)

⇒ Y joined after 2 days, both of them worked together for 6 days, = (2 + 1) x 6 = 18 units,

⇒ Remaining work = 92 - (18 + 4) = 70 units.

⇒ Remaining work is completed by all of them together in = \(\frac{70}{(2+1+4)}\) = \(\frac{70}{(7)}\) = 10 days.

⇒ Total time taken to complete to comlete the work = 2 + 6 + 10 = 18 days.

As, X was doing the work since day 1, therefore he worked for 18 days.