A, B and C can do piece of work in 30 days, 45 days and 90 days, respectively. A starts the work and he is assisted by B and C together on every third day. In how many days will the work be completed?

23

A = 30 days, B = 45 days, C = 90 days,

⇒ Since A is working daily and B & C assist him on every third day, the efficiencies will be as follows:

1st day (A) = 3 units

2nd day (A) = 3 units

3rd day (All) = 3 + 2 + 1 = 6 units

Every 3 days work = 3 + 3 + 6 = 12 units.

Hence, in 21 days, 84 units of work will be completed.

and in 23 days. 90 units of work will be completed.

Therefore, time taken to complete the total work will be 23 days.