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
Question
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
Solution
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.
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