The question is from Pipes and Cisterns: Filling Tank. Time required to fill a tank by three pipes are given. Tank is filled to a certain level, how long it would take to fill the tank? Mathematicians are creatures of habit. This topic has been called Pipes and Cisterns because someone named it like it long ago. Pipes and Tanks would be much better - at least makes it sound like wartime.
Question 7: Pipes A, B and C can fill a tank in 30, 60 and 120 minutes respectively. Pipes B and C are kept open for 10 minutes, and then Pipe B is shut while Pipe A is opened. Pipe C is closed 10 minutes before the tank overflows. How long does it take to fill the tank?
Let us assume that the tank has a capacity of 120 litres. So, the pipes discharge the following amounts of water:
(A) 4 litres per minute
(B) 2 litres per minute
(C) 1 litre per minute.
Part 1: B and C (3 litres/min) are kept open for 10 minutes, filling 3 × 10 = 30 litres. 90 litres remain to be filled in the tank.
Part 2: Now, B is shut and A is opened. Effectively, this means that A and C are filling the tank together (5 litres / minute). We don’t yet know how long A and C are open together.
Part 3: C is closed 10 minutes before the tank overflows. This means that only A works for the last 10 minutes, filling 40 litres (working@4 litres/min)
Since 30 litres are filled in Part 1 and 40 litres in Part 3, the balance (50 litres) should have been filled in Part 2.
Working together, A and C fill 5 litres per minute in Part 2. This means that they would have taken 10 minutes to fill 50 litres.
So, the entire time it took to fill the tank is:
10 + 10 + 10 = 30 mins.
In one minute, A fills (1/30)th of the tank, B fills (1/60)th of the tank, and C fills (1/120)th of the tank.
(B + C) work for 10 minutes, followed by (A + C), which works for “t” minutes, followed by A, which work for 10 minutes. This ensures that the tank gets filled. This can be written in an equation form:
10 * (1/60 + 1/120) + t * (1/30 + 1/120) + 10 * (1/30) = 1
10 * (1/40) + t * (1/24) + 10 * (1/30) = 1.
Or, 1/4 + t/24 + 1/3 = 1. Or t = 10.
So, the entire tank was filled in 30 mins.
The question is "How long does it take to fill the tank?"
Choice C is the correct answer.
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