Aptitude Questions: Pipes & Cistern Set 7

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Questions Penned by Yogit

1. A pipe can empty a tank in 60 minutes alone. Another pipe whose diameter is twice the diameter of first pipe is also opened. Now find the time in which both pipe will empty the tank together.
   a) 8 min
   b) 10 min
   c) 12 min
   d) 14 min
   e) None of these
   
   Answer & Explanation

   Answer – c) 12 min
   Explanation :
   Time taken by pipe to empty the tank is inversely proportional to cross- sectional area.
   So, time taken by second pipe will be = 60/4 = 15 min (πr2 = 1/60 and  for second pipe 4πr2 = 1/T so we get T = 15 min)
   Time taken by both to empty the pipe = (60*15)/75 = 12
   
   
   
2. Two pipes P and Q can fill a tank in 10 min and 12 min respectively and a waste pipe can carry off 12 litres of water per minute. If all the pipes are opened when the tank is full and it takes one hour to empty the tank. Find the capacity of the tank.
   a) 30
   b) 45
   c) 60
   d) 75
   e) None of these
   
   Answer & Explanation

   Answer – c) 60
   Explanation :
   Let the waste pipe take ‘T’ time to empty the tank.
   (1/10 + 1/12 – 1/T)*60 = -1
   We will get T = 5 min
   So capacity = 5*12 = 60ltr
   
   
   
3. Two pipes P and Q can fill a tank in 36 and 24 minutes respectively. If both the pipes are opened simultaneously, after how much time pipe Q should be closed so that tank is full in 30 minutes.
   a) 2min
   b) 4min
   c) 6min
   d) 8min
   e) None of these
   
   Answer & Explanation

   Answer – b) 4min
   Explanation :
   Let after T time, Q is closed, (1/36 + 1/24)*T + (1/36)*(30 – T) = 1
   
   
   
4. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. Both the pipes are opened together but after 5 minutes pipe B is closed. What is the total time required to fill the tank
   a) 16.1/3 min
   b) 16.2/3 min
   c) 17.2/3 min
   d) 18.2/3 min
   e) None of these
   
   Answer & Explanation

   Answer – b) 16.2/3 min
   Explanation :
   (1/20 + 1/30)*5 + (1/20)*T = 1
   total time = T + 5 min
   
   
   
5. Three pipes P, Q and R can fill a tank in 12, 15 and 20 minutes respectively. If pipe P is opened all the time and pipe Q and R are opened for one hour alternatively. The tank will be full in
   a) 5hr
   b) 6hr
   c) 7hr
   d) 8hr
   e) None of these
   
   Answer & Explanation

   Answer – c) 7hr
   Explanation :
   (1/12 + 1/15) + (1/12 + 1/20) = 17/60 (in 2 hrs this much tank is filled)
   so in 6 hrs 51/60 is filled. Remaining, 9/60 = (1/12 + 1/15)*t, so T = 1hr
   so total = 6 + 1 = 7 hr
   
   
   
6. A cistern can be filled by a pipe in 6 hours. A leak is developed at the bottom due to which it takes 2 hours more to fill the cistern. Find the time taken by the leak to empty the cistern when the cistern is full.
   a) 20hr
   b) 22hr
   c) 24hr
   d) 26hr
   e) None of these
   
   Answer & Explanation

   Answer – c) 24hr
   Explanation :
   1/6 – 1/T = 1/8, solve for T
   
   
   
7. A pipe can fill a tank in 20 minutes and another pipe can fill the tank in 40 minutes. There is a waste pipe which can empty the tank in 15 minutes. First two pipes are opened for 5 minutes and then the third pipe is also opened. In what time the cistern is emptied after the third pipe also opened
   a) 60
   b) 75
   c) 80
   d) 90
   e) None of these
   
   Answer & Explanation

   Answer – b) 75
   Explanation :
   (1/20 + 1/40)*5 + (1/20 + 1/40 – 1/15)*T = 1
   
   
   
8. Two pipes can separately fill the tank in 15hrs and 30hrs respectively. Both the pipe are opened and when the tank is 1/3 full a leak is developed due to which 1/3 water supplied by the pipe leaks out. What is the total time to fill the tank?
   a) 20/3 hr
   b) 35/3 hr
   c) 40/3 hr
   d) 50/3 hr
   e) None of these
   
   Answer & Explanation

   Answer – c) 40/3 hr
   Explanation :
   (1/15 + 1/30)*T1 = 1/3, T1 = 10/3 hr
   now after leak is developed, [(1/15 + 1/30) – (1/3)*(1/15 + 1/30)]*T2 = 2/3
   T2 = 10 hr. So total time = 10 + 10/3 = 40/3 hr
   
   
   
9. Pipe P is 4 times as fast as Q in filling a tank. If P takes 20 minutes to fill a tank, then what is the time taken by both the pipe P and Q to fill the tank?
   a) 12
   b) 16
   c) 18
   d) 20
   e) None of these
   
   Answer & Explanation

   Answer – b) 16
   Explanation :
   P takes 20 minutes and it is 4 times faster than Q, it means Q will take 80 minutes to fill the tank.
   (1/20 + 1/80)*t = 1. We get t = 16
   
   
   
10. In what time a cistern is filled by three pipes of diameter 2cm, 4cm and 6cm respectively. If the time taken by largest pipe to fill the tank is 40 minutes. Amount of water flowing through the pipe is proportional to the diameter of the pipe
    a) 25.5/7 min
    b) 25.3/7 min
    c) 23.5/7 min
    d) 23.4/7 min
    e) None of these
    
    Answer & Explanation

    Answer – a) 25.5/7 min
    Explanation :
    Larger the cross-section area less will be time taken by pipe to fill the tank.
    36/16 = T/40, T = 90min (for 4 cm pipe)
    similarly for 2 cm pipe time taken will be = 360min
    Total time = (1/360 + 1/90 + 1/40) = 1/p, so we get P = 25.5/7 minutes