Question
A, B, and C can complete a job in 15, 20, and 30 days,
respectively. They start the work together but after 3 days, A leaves. Then, B works alone for 5 days, after which D joins B. Together, B and D complete the remaining work in 1.5 days. How many days will it take for D to finish the entire job alone?Solution
Let the total work be represented as 1 unit. Work done by A per day = 1/15, Work done by B per day = 1/20, Work done by C per day = 1/30. In the first 3 days, A, B, and C work together: Work done in 3 days = 3 × (1/15 + 1/20 + 1/30) = 3 × (4/60 + 3/60 + 2/60) = 3 × 9/60 = 27/60 = 9/20 of the work. After 3 days, remaining work = 1 - 9/20 = 11/20 of the work. Now, B works alone for 5 days: Work done by B in 5 days = 5 × (1/20) = 5/20 = 1/4 of the work. Remaining work after 5 days = 11/20 - 1/4 = 11/20 - 5/20 = 6/20 = 3/10. In the next 1.5 days, B and D work together: Work done by B and D together in 6 days = 1.5 × (1/20 + 1/D) 1.5 × (1/20 + 1/D) = 3/10 1/20 + 1/D = 1/5 Work done by D per day = 3/20, Time taken by D to finish the entire work = 1 / (3/20) = 20/3 days.
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