If pipe A can fill a cistern in X hours, pipe B can fill the same cistern in Y hours, and pipe C can empty the full cistern in Z hours, then find the time taken to completely fill the cistern, if Pipes A, B and C are opened together.

1
\(\rm \frac{XYZ}{YZ-XZ- XY}\)
2
\(\rm \frac{XYZ}{YZ+XZ+ XY}\)
3
\(\rm \frac{XYZ}{YZ+XZ- XY}\)
4
\(\rm \frac{XYZ}{YZ-XZ+XY}\)

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