Shortcut of Pipes and Cisterns

Shortcut 73:
One pipe fills and another empties
\frac{AB}{-A+B}
Question:
Pipe A can fill a tank in 4 hours and pipe B can empty the tank in 5 hours. If both pipes are opened together, how long will they take to fill a complete tank?
Answer:
A = 4
B = 5
Substitute the values in the above equation, we get
Time taken to fill the tank = (4 x 5)/(-4 + 5)
= 20 hours

Shortcut 74:”
Two pipes fill and one empties the tank
\frac{ABC}{-AB+BC+AC}
Question:
Pipes A and B can fill a tank in 10 hours and 12 hours respectively. Pipe C can empty a tank in 20 hours. If all the pipes are opened together, how long will they take to fill a complete tank?
Answer:
A = 10
B = 12
C = 20
Substitute the values in the above equation, we get
Time taken to fill the tank
= (10 x 12 x 20 )/[(-10 x 12) + (12 x 20) + (10 x 20)]
= 7. 5 hours
= 7 hours 30 minutes

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