Description for Correct answer:
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