A, B and C can do a piece of work in 11, 20 and 55 days respectively. In how many days work will be finished if A is assisted by B and C on alternative day

Sure, let's solve this step by step:

Step 1: First, we need to find out the one day's work of A, B and C.

A's one day work = 1/11 B's one day work = 1/20 C's one day work = 1/55

Step 2: Now, let's find out the work done by A, B and C in two days (since B and C are working on alternate days).

Two days work = A's one day work + B's one day work + A's one day work + C's one day work = 1/11 + 1/20 + 1/11 + 1/55 = 2/11 + 1/20 + 1/55

Step 3: Calculate the above expression:

Two days work = (4 + 1 + 1) / (220) = 6/220 = 3/110

So, A, B and C together can finish the work in two days is 3/110.

Step 4: Now, we need to find out the total time taken to complete the work. Since they are completing 3/110 of the work in 2 days, the total time taken to complete the work would be:

Total time = (Total work / Work done in two days) * 2 = (1 / (3/110)) * 2 = 110/3 * 2 = 220/3 days

So, the work will be finished in 220/3 days or approximately 73.33 days if A is assisted by B and C on alternate days.