Pipe A can fill a tank in $12\text{ hours}$, while Pipe B can fill it in $15\text{ hours}$. Pipe C can empty the full tank in $20\text{ hours}$. If all three pipes are opened simultaneously, the time taken in hours to fill the empty tank completely is ________ (answer in integer).
Answer Key:
10
Step-by-Step Solution & Explanation
Let the capacity of the tank be the LCM of $(12, 15, 20) = 60\text{ units}$.
• Pipe A filling rate $= \frac{60}{12} = +5\text{ units/hour}$
• Pipe B filling rate $= \frac{60}{15} = +4\text{ units/hour}$
• Pipe C emptying rate $= \frac{60}{20} = -3\text{ units/hour}$
Net rate of work $= 5 + 4 - 3 = 6\text{ units/hour}$.
Time required to fill tank $= \frac{60\text{ units}}{6\text{ units/hour}} = 10\text{ hours}$.