A, B and C can do a piece of work in 10, 15 and 30 days, respectively. If B and C both assist A on every third day,then in how many days can the work be completed?

Let the total work done by A,B and C is 30 units. (LCM of 10,15 and 30)

Efficiency = one day work

$$efficiency\ =\ \frac{total\ work}{time\ taken}$$

Efficiency of A,B and C is 3,2 and 1 unit respectively

Work done by A in first two days = $$3\times\ 2=6$$

Work done on 3rd day = (3 + 2 + 1) = 6 

total work done in 3 days = 6 + 6 = 12

work done in next 3 days = 12 

Total work till end of the 6th day = 12 + 12 = 24

Remaining work = 30 - 24 = 6

so, A alone will do 6 unit work in next two days ( as B and C assist A on every 3rd day)

So total work finish in 6 + 2 = 8 days.