Question

A tap can fll a tank in 6 bours. After half the tank is filled, three more similar taps. Are opened. What is the total time taken to fill the tank completely ?

Answer 1

Answer:

Let Volume of tank = V liters

Time taken by the tap to fill the tank = 6 hours

Amount of water in tank after 1 hour $=\frac{V}{6}$

Amount of water in tank after 3 hours $=\frac{V}{2}$

Three more similar taps are opened ,each having individual capacity to fill the tank in 6hours.

Let total time taken by 3 taps together to fill the tank be x hours.

$\frac{V}{2}+x\frac{V}{6}=V\\\\ x\frac{V}{6}=V-\frac{V}{2}\\\\ x\frac{V}{6}=\frac{V}{2}\\\\x=3$

Total time taken by 3 taps together to fill the tank = 3 Hours