Question

Pipes A and B can fill a tank in 16 hours and 24 hours, respectively, whereas pipe C can empty the full tank in 40 hours. All three pipes are opened together, but pipe A is closed after 10 hours. After how many hours will the remaining part of the tank be filled?

• A. 10
• B. 20
• C. 12 1/2
• D. 15 1/2

Answer 1

Answer:

C. 12 1/2

Solution: Given: Pipe A can fill in 16 hours Pipe B can fill in 24 hours Pipe C can empty in 40 hours Concept used: If a pipe can fill or empty in A hours, then it can fill or empty 1/A part in 1 hour. Calculation: Pipe A can fill 1/16 in 1 hour Pipe B can fill 1/24 in 1 hour Pipe C can empty 1/40 in 1 hour Together they can fill 1/16 + 1/24 – 1/40 part in 1 hour ⇒ Together they can fill 19/240 parts in 1 hour ⇒ Together they can fill 190/240 = 19/24 part in 10 hours Remaining tank = 1 – 19/24 = 5/24 B and C can do 1/24 – 1/40 = 2/120 = 1/60 B and C can fill a tank in 60 hours B and C can fill 5/24 tank in 60 × 5/24 = 25/2 = 12 1/2 hours