CAT Practice : Pipes cisterns, Work time

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A Classic pipes and tanks question !!

Pipes Cisterns - Filling Tanks

    Q.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?
    1. 40 minutes
    2. 28 minutes
    3. 30 minutes
    4. 36 minutes


  • Correct Answer
    Choice C. 30 minutes

Explanatory Answer

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Detailed Solution

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.
Answer choice (c)

Alternate Solution

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 x (1/60 + 1/120) + t x (1/30 + 1/120) + 10 x (1/30) = 1
10 x (1/40) + t x (1/24) + 10 x (1/30) = 1.
Or, 1/4 + t/24 + 1/3 = 1. Or t = 10.
So, the entire tank was filled in 30 mins.

Answer choice (C).

Correct Answer: 30 minutes

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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.