X and Y together can do a piece of work in 30 days. Z alone can do it in 60 days. If they worked together, then in how many days can they finish the work?

20 days

Total work = LCM of 30, 60 = 60

Efficiency of X+Y+Z = eff(X+Y) + eff(Z)

                              = 2 + 1= 3

Time taken by X, Y, Z together to complete the work = $\frac{total\;work}{efficiency}$

                                                                             = $\frac{60}{3}$ = 20 days