A, B, C and D when working alone can complete a piece of work in 10, 12, 15 and 20 days, respectively. A and C start the work. After 2 days, D replaced A. After 2 more days, B replaced C. After 2 more days, A comes back and replaces B. How many days from the start will be taken by them to finish the work?

Let the total work be 60 units, making the efficiencies of A, B, C and D equal to 6, 5, 4 and 3 units per day respectively. In the first 2 days A and C complete 2 times 10 units, in the next 2 days C and D complete 2 times 7 units, and in the following 2 days B and D complete 2 times 8 units, bringing the total work done to 50 units. After these 6 days, the remaining work is 10 units, which A and D complete at a combined rate of 9 units per day. Dividing the 10 remaining units by 9 units per day gives 10/9 days, and adding this to the initial 6 days results in 64/9 days.

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