Aptitude Questions: Pipes & Cistern Set 6

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1. Two pipes P and Q can fill a tank in 20hrs and 25hrs respectively while a third pipe R can empty the tank in 30hrs. If all the pipes are opened together for 10hrs and then pipe R is closed then in what time the tank can be filled.
   a) 400/23hrs
   b) 400/27hrs
   c) 200/23hrs
   d) 200/27hrs
   e) None of these
   
   Answer & Explanation

   Answer – b) 400/27hrs
   Explanation :
   (1/20 + 1/25 – 1/30)*10 + (1/20 + 1/25)*x = 1
   We get x = 130/27, so total time to fill the tank = 130/27 + 10 = 400/27 hrs
   
   
   
2. There are three taps A, B and C which can fill a tank in 12hrs, 15hrs and 30 hrs respectively. If the tap A is opened first, after one hour tap B was opened and after 2 hours from the start of A, tap C is also opened. Find the time in which the tank is full.  
   a) 6(2/11)hr
   b) 6(3/11)hr
   c) 5(3/11)hr
   d) 5(2/11)hr
   e) None of these
   
   Answer & Explanation

   Answer –a) 6(2/11)hr
   Explanation :
   In first hour only A is opened, in the next hour A and B are opened and in the third hour A, B and C are opened.
   So, in three hours (3/12 + 2/15 + 1/30) = 25/60 tank is already filled.
   Now, 25/60 = (1/12 + 1/15 + 1/30)*t
   T = 25/11. Total time = 3 + 25/11 = 58/11 hours
   
   
   
3. Three pipes P, Q and R can fill the tank in 5, 10 and 15 minutes respectively. If all the pipes are opened together and pipe Q is turned off 5 minutes before the tank is fill. Then find the time in which the tank will full.
   a) 45/11hrs
   b) 53/11hrs
   c) 51/13hrs
   d) 47/11hrs
   e) None of these
   
   Answer & Explanation

   Answer – a) 45/11hrs
   Explanation :
   Let total time taken by the pipes is T hrs, then
   (1/5 + 1/10 + 1/15)*(T – 5) + (1/5 + 1/15)*5 = 1
   
   
   
4. A pipe can fill a tank in 20 minutes but due to a leak develop at the bottom of the tank, 1/5 of the water filled by the pipe leaks out. Find the time in which the tank is filled.
   a) 20 min
   b) 25 min
   c) 30 min
   d) can’t be determined
   e) None of these
   
   Answer & Explanation

   Answer – b) 25 min
   Explanation :
   Amount of tank filled by the pipe in one minute = 1/20 and due to leakage 1/5 of 1/20 leaks out so, [1/20 – (1/5)*(1/20)]*T = 1
   We get T = 25
   
   
   
5. A bathing tub can be filled by a cold pipe in 15 minutes and by a hot pipe in 10 minutes. Ramesh opened both the tap and leaves the bathroom and returns at the time when the tub should be full. He observed that a waste pipe is opened at the bottom, he now closes it. Now the tub will take more 5 minutes to fill the tank, find the time in which the leak can empty the tank.
   a) 36/5 min
   b) 33/5 min
   c) 37/5 min
   d) can’t be determined
   e) None of these
   
   Answer & Explanation

   Answer – a) 36/5 min
   Explanation :
   (1/15 + 1/10 – 1/x)*6 + (1/15 + 1/10)*5 = 1
   x = 36/5
   
   
   
6. There are 10 taps connected to a tank. Some of them are waste pipe and some of them are water pipe. Water pipe can fill the tank in 15 hours and waste pipe can empty the tank in 30 hours. Find the number of waste pipes if the tank is filled in 6 hours.
   a) 3
   b) 4
   c) 5
   d) 7
   e) None of these
   
   Answer & Explanation

   Answer – c) 5
   Explanation :
   Let water pipes are x and waste pipe are Y.
   x + y = 10
   (x/15 – y/30)*6 = 1
   Solve both equation to get x and y
   
   
   
7. Pipe A is 4 times as fast as B in filling a tank. If A takes 20 minutes to fill a tank, then what is the time taken by both the pipe A and B to fill the tank?
   a) 12
   b) 16
   c) 18
   d) 20
   e) None of these
   
   Answer & Explanation

   Answer – b) 16
   Explanation :
   A takes 20 minutes and it is 4 times faster than B, it means B will take 80 minutes to fill the tank.
   (1/20 + 1/80)*t = 1. We get t = 16
   
   
   
8. Pipe A is 4 times faster than pipe B and takes 45 minutes less to fill a tank. When both the pipes are opened together than the time in which the tank will be full.
   a) 10 min
   b) 12 min
   c) 15 min
   d) 18 min
   e) None of these
   
   Answer & Explanation

   Answer – b) 12 min
   Explanation :
   Let A take X minute to fill a tank then B will take 4x time.
   4x – x = 45 (given), X = 15.
   Time taken to fill the tank together = (1/15 + 1/60)*t =1
   T = 12 minute
   
   
   
9. Two pipes P and Q can fill a tank in 20 minutes and 30 minutes respectively. There is a waste pipe which withdraws water at the rate of 8 litres per minute. Now the tank is full and If all the pipes are opened simultaneously the tank is emptied in 60 minutes. Find the capacity of the tank.
   a) 60ltr
   b) 70ltr
   c) 80ltr
   d) 90ltr
   e) None of these
   
   Answer & Explanation

   Answer – c) 80ltr
   Explanation :
   (1/20 + 1/30 – 1/t)*60 = -1
   ‘-1’ is taken because the work is negative.  T is the time taken by the waste pipe to empty the tank alone. We will t = 10
   So capacity = 10*8 = 80ltr
   
   
   
10. There are 4 filling pipes and 3 emptying pipes capable of filling and emptying in 12 minutes and 15 minutes respectively. If all the pipes are opened together and as a result they fill 10 litres of water per minute. Find the capacity of the tank.
    a) 65ltr
    b) 70ltr
    c) 75ltr
    d) 80ltr
    e) None of these
    
    Answer & Explanation

    Answer – c) 75ltr
    Explanation :
    (4/12 – 3/15)*t = 1
    t = 15/2 minute – in this time the tank will be filled. So the capacity = (15/2)*10 = 75 litre