Question
Pipe βPβ and pipe βQβ can fill a tank alone in
40 hours and 60 hours, respectively. If pipe βPβ and pipe βQβ were opened together and pipe βPβ was closed after 20 hours, then find the time taken by pipe βQβ to fill the remaining portion of the tank alone.Solution
Let the capacity of the tank be 120 units (LCM of 40 and 60) Efficiency of pipe βPβ
= 120 Γ· 40
= 3 unit/hour Efficiency of pipe βQβ
= 120 Γ· 60
= 2 unit/hour Let the pipe βQβ fill the remaining portion of the tank in x hours. ATQ, 20 Γ (3 + 2) + 2x = 120 Or, 20 Γ 5 + 2x = 120 Or, 100 + 2x = 120 Or, 2x = 20 Or, x = 10 Therefore, required time taken by pipe βQβ = 10 hours
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