A tank is half full. Outlet pipes A and B can empty the full tank in 6 hours and 12 hours respectively, and inlet pipe C can fill the empty tank in 8 hours. Which of the following statements are correct?
(A) If only A and B are opened, the tank becomes empty in 2 hours.
(B) If all three pipes are opened, the tank becomes empty in 4 hours.
(C) If only A and C are opened, the tank becomes empty in 12 hours.
(D) If only B and C are opened, the tank becomes full in 24 hours.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B) and (C) only
In 1 hour, A takes out \(\frac{1}{6}\) of the tank, B takes out \(\frac{1}{12}\) and C puts in \(\frac{1}{8}\). Only half the tank has to be emptied or filled.
\(\displaystyle \text{A and B}: \frac{1}{6} + \frac{1}{12} = \frac{1}{4} \text{ out per hour}\)
\(\displaystyle \text{A, B and C}: \frac{1}{4} - \frac{1}{8} = \frac{1}{8} \text{ out per hour}\)
\(\displaystyle \text{A and C}: \frac{1}{6} - \frac{1}{8} = \frac{1}{24} \text{ out per hour}\)
\(\displaystyle \text{B and C}: \frac{1}{8} - \frac{1}{12} = \frac{1}{24} \text{ in per hour}\)
So, for the half tank, A and B take 2 hours, all three take 4 hours, A and C take 12 hours to empty it, and B and C take 12 hours to fill it.
Checking the statements
(A) If only A and B are opened, the tank becomes empty in 2 hours. — Correct. Half the tank at \(\frac{1}{4}\) per hour takes 2 hours.
(B) If all three pipes are opened, the tank becomes empty in 4 hours. — Correct. Half the tank at \(\frac{1}{8}\) per hour takes 4 hours.
(C) If only A and C are opened, the tank becomes empty in 12 hours. — Correct. Half the tank at \(\frac{1}{24}\) per hour takes 12 hours.
(D) If only B and C are opened, the tank becomes full in 24 hours. — Incorrect. Only half the tank is to be filled, so at \(\frac{1}{24}\) per hour it takes 12 hours.