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.

Correct option is A

Given:

Pipe A can fill the cistern in X hours.

Pipe B can fill the cistern in Y hours.

Pipe C can empty the cistern in Z hours.

Solution:

The rate of filling or emptying is given as:

Pipe A's rate = $$\frac{1}{X}$$​​ (cistern per hour)

Pipe B's rate = $$\frac{1}{Y}$$​ (cistern per hour)

Pipe C's rate (emptying) = $$-\frac{1}{Z}$$​ (cistern per hour, since it empties)

The combined rate:

​$$= \frac{1}{X} + \frac{1}{Y} - \frac{1}{Z} \\ \ \\ = \frac{YZ+XZ-XY}{XYZ}$$​​

Thus, time taken = $$\frac{XYZ}{YZ+XZ-XY}$$​​