Question: An inlet tap can fill a tank in 20 hours. This tap was opened at time zero, but after 4 hours (t = 4), a leak developed at the bottom. After 8 hours (t = 8), the cross section of the leak became triple because of which, it took 30 hours to fill the tank. How much time will it take to fill the tank if the cross section of the hole does not change at t = 8?
[Type in your answer as the nearest possible integer in seconds.]
Let the hole formed initially can empty the entire tank in x hours.
After the cross section triples, it empties the entire tank in x/3 hours.
The inlet pipe worked for 30 hours. The outlet pipe worked for 4 hours at normal efficiency and then worked for another 22 hours at three times the efficiency.
⇒ x = 140 hours.
Now had the cross section not changed let’s say it would’ve taken t hours to fill the tank.
∴ The inlet pipe works for t hours, whereas the outlet pipe works at normal efficiency for (t – 4) hours.
⇒ t = 136/6 = 81600 seconds.
Hence, 81600.