Question
Machine X is 100% more efficient than Machine Y, and
Machine Y is 75% more efficient than Machine Z. Machines X and Z, working together, can complete a certain task in 15 days. How many days will it take for Machines Y and Z, working together, to complete twice the amount of work, if Machine Z operates at only half of its normal efficiency?Solution
Let the efficiency of 'Z' be 4x units/day. So, efficiency of 'Y' = 4x X (7/4) = 7x units/day And, efficiency of 'X' = 14x units/day So, total work = (14x + 4x) X 15 = '270x' units Therefore, required time = (2 X 270x) ÷ (7x + 0.5 X 4x) = (570x/9x) = 60 days
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