Pipe And Cistern

• The first statement "Some men are wise" means there exists a subset of men who possess wisdom.
• The second statement "All wise are professors" indicates that every individual who is wise also fits into the category of professors.

To solve the problem, we need to calculate the total time taken by both pipes A and B to fill the cistern with the condition that pipe B is turned off after 5 minutes.

First, let's determine their individual rates of filling the cistern:

• Pipe A takes 15 minutes to fill the cistern. Thus, its rate is of the cistern per minute.
• Pipe B takes 30 minutes to fill the cistern. Thus, its rate is of the cistern per minute.

When both pipes are opened together for the first 5 minutes, their combined rate is:

So, in 5 minutes, they fill:

of the cistern.

After 5 minutes, pipe B is turned off, and only pipe A continues to fill the cistern. At this point, half of the cistern is already filled, so half remains. Pipe A will take additional time to fill the remaining cistern:

Pipe A fills of the cistern per minute. To fill the remaining , it requires:

minutes.

Therefore, the total time= 5 + 7.5= 12.5 minutes