Question
X can build a wall in 15 days, Y can build same wall in
25 days and Z can destroy the same wall in 30 days. If X & Y worked together for P days after that Z joined them. Now they all together completed the rest of the work in (P+15/11) days. In how many days total work will be completed?Solution
Let total work = LCM(15, 25, 30) = 150 units So, ratio of 1 day work by X, Y & Z respectively = 10 : 6 : (-5) According to question, P(10+6) + (P+15/11) × (10+6-5) = 150 16P + (P+15/11) × (11) = 150 16P + 11P + 15 = 150 27P = 135 P = 5 So total days = P + (P + 15/11)             = 5 + 5 + 15/11            = 10 + 15/11 = 125/11 days.
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