A full water tank has two drain valves at the bottom. The first valve alone can empty the tank in 10 hours and the second valve alone in 40 hours. No water flows into the tank. If both valves are opened together, how long will the tank take to become empty?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 8 hours
Take the capacity of the tank as the LCM of 10 and 40, that is 40 units. Two outlets open together add the units they drain each hour, just as two filling pipes add the units they fill.
First valve: \(40\div10=4\) units per hour
Second valve: \(40\div40=1\) unit per hour
Both together: \(4+1=5\) units per hour
Time to empty the full tank \(=40\div5=8\) hours
The tank becomes empty in 8 hours.