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# A tank has 3 inlets X, Y and Z and 1 outlet. P, Y fills the empty tank in 3 times the time taken by Z to fill the empty tank completely. X fills the empty tank completely in 1.5 times the time taken by Y to fill the empty tank completely. Also, Z fills the empty tank completely in half the time taken by P to empty the full tank completely. If the time taken to fill the empty tank completely when all of them are opened simultaneously is $$\Large 3 \frac{15}{19}$$ hours. how much time (in hours) will P take to empty the full tank completely ?

 A) $$\Large 6 \frac{1}{2}$$ B) 6 C) 8 D) 4

 C) 8

Let time taken by pipe Z in filling the empty tank = x hours

$$\Large \therefore$$ Time taken by Y = 3x hours

$$\Large \therefore$$ Time taken by X

=> $$\Large (\frac{3}{2} \times 3x) \ hours$$

= $$\Large \frac{9x}{2} \ hours$$

Time taken by P in emptying the full tank = 2x hours

According to the question,

$$\Large \frac{1}{x} + \frac{1}{3x} + \frac{2}{9x} - \frac{1}{2x} = \frac{19}{72}$$

=> $$\Large \frac{18 + 6 + 4 - 9}{18x} = \frac{19}{72}$$

=> $$\Large \frac{19}{18x} = \frac{19}{72} => 18x = 72$$

=> $$\Large x = \frac{72}{18} = 4 \ hours$$

$$\Large \therefore$$ Time taken by P in emptying the tank = 8 hours

Part of solved Aptitude questions and answers : >> Aptitude

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