A tank has two outlet pipes, A and B, which together take 6 hours to empty a full tank when they are opened simultaneously. The tank was initially half-full and both the outlets were opened, after an hour an inlet pipe was also opened. If the inlet alone can fill the empty tank in 4 hours, how much time will it now take to fill the tank completely?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8 hrs
Note: The given answer is as per the official NTA Answer Key. However, the time can also be counted from the start, and with that reading Option (1) could also be a possible answer, as explained below.
Let the capacity of the tank be 1 unit. The rates per hour are:
Outlets A and B together: \(\frac{1}{6}\) per hour (emptying)
Inlet: \(\frac{1}{4}\) per hour (filling)
In the first hour only the outlets are open:
\( \displaystyle \frac{1}{2} - \frac{1}{6} = \frac{1}{3} \) of the tank is left
With all three pipes open:
\( \displaystyle \text{Net rate} = \frac{1}{4} - \frac{1}{6} = \frac{1}{12} \) per hour (filling)
\( \displaystyle \text{Time} = \frac{1 - \frac{1}{3}}{\frac{1}{12}} = \frac{2}{3} \times 12 = 8 \) hours
Option (1) 9 hrs — Should also be correct, though not the answer given by NTA. The question asks for the time needed to fill the tank, but does not say from when the time is counted. If it is counted from the very start, when only the outlets were opened, the tank takes
1 hour (outlets only, tank goes from half full to one-third full)
+ 8 hours (all three pipes, tank goes from one-third full to full)
= 9 hours in all
Option (2) 8 hrs — Correct. The question says “how much time will it now take”, and “now” is the moment the inlet is opened. From that moment the remaining \(\frac{2}{3}\) of the tank fills at \(\frac{1}{12}\) per hour, which takes 8 hours.
Option (3) 6 hrs — Incorrect. This is the time the two outlets take to empty a full tank.
Option (4) 11 hrs — Incorrect. It matches neither reading.