Question
A, B, and C can complete a work in 12, 16, and 24 days
respectively. B and C worked together for 4 days then C left work and A replaced him. In how many days will the remaining work be completed?Solution
LCM of 12, 16 and 24 is 48. Efficiency of A = (48/12) = 4 units/day Efficiency of B = (48/16) = 3 units/day Efficiency of C = (48/24) = 2 units/day Time taken by B and C together for 4 days = [4 x (3 + 2)] = (4 x 5) = 20 units The remaining work = (48-20) = 28 units Now, Time taken by B and A to complete the remaining work = [28/ (3 + 4)] =28/7 days = 4 days The required time is 4 days.
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