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    Question

    Two pipes X and Y can fill an empty tank in 8 hours and

    10 hours, respectively. Pipe Z alone can empty the completely filled tank in 15 hours. Firstly, both pipes X and Y are opened, and after 4 hours, pipe Z is also opened. What will be the total time (in hours) required to completely fill the tank?
    A 89/29 Correct Answer Incorrect Answer
    B 89/19 Correct Answer Incorrect Answer
    C 88/19 Correct Answer Incorrect Answer
    D 88/29 Correct Answer Incorrect Answer

    Solution

    Pipe X fills in 8 hours → rate = 1/8 Pipe Y fills in 10 hours → rate = 1/10 Pipe Z empties in 15 hours → rate = 1/15 For the first 4 hours, only X and Y work:(1/8 + 1/10) × 4 = 9/40 × 4 = 36/40 = 9/10 So, 90% of the tank is filled. Now X, Y, and Z work together: (1/8 + 1/10 + 1/15) = 19/120 ​Remaining work =  1 − 9/10 = 1/10​ Time to finish =  (1/10)/(19/120) = 12/19 hrs Total time =  4 + 12/19 = 88/19 hrs

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