X, Y and Z can complete a piece of work in 46 days, 92 days and 23 days, respectively. X started the work. Y joined him after 7 days. If Z joined them after 8 days from the beginning, then for how many days did Y work?

$11 \frac{5}{7}$

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

⇒ Here, X worked alone for 7 days ⇒ 2 x 7 = 14 units  ..(Efficiency × Days = Work)

⇒ Y joined after 7 days, both of them worked together for 1 days, = (2 + 1) x 1 = 3 units,

⇒ Remaining work = 92 - (14 + 1) = 75 units.

⇒ Remaining work is completed by all of them together in = \(\frac{75}{(2+1+4)}\) = \(\frac{75}{(7)}\) = \( { 10}_{ 7}^{ 5} \) days.

⇒ Total days of work Y worked = \( { 10}_{ 7}^{ 5} \) + 1 = \( { 11}_{ 7}^{ 5} \) days.