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Pipe and cisterns math tricks

 Pipe and tank questions are solved in the same way as time and work questions are solved.

 Here very short and long method have also been used so that the preparation of your examinations can be done easily.

 In L.C.M method, L.C.M is the total capacity of the tank or the total amount of water to be filled.


 The following tricks will be used to solve the questions of pipes and tanks:-


 A) Pipe A takes y time to fill a tank and Pipe B takes x time to fill that tank.  In how much time will the tank be filled if both are opened together?


 T  = {(xy)÷(x+y)}


 B) Pipe A takes x time to fill a tank and Pipe B takes y time to empty that tank.  How long will it take to fill the tank if both the pipes are opened simultaneously?


 T= {(xy)÷(y-x)}


 C) Pipes A and B fill a tank in x and y time respectively.  Pipe C takes z time to empty the tank. If all three are opened together, then how much time will it take to fill the tank?


 T={(x×y×-z)}÷(xy-yz-zx)}


 Since z is the emptying time. So z is taken as a minus.


 D) Pipes A, B and C take x, y and z time respectively to fill a cistern.  How long will it take to fill the tank if all three are opened together?


 T = {(xyz)÷ (xy+yz+zx)}


 Q.1)  Pipe A can fill a tank in 5 hours and Pipe B can fill that tank in 8 hours.  In how much time they together will be able to fill the tank?

 Solution:- (5×8)÷(5+8)= 40÷13

                                       = 3.07 hours ans.

 L.C.M Method:- 

1) L.C.M = 40 of 5 and 8 (Total capacity in the tank)

2) A pours 40 liters of water into the tank in 5 hours.

 Pours in 1 hour = 40/5 = 8 liters

 3) B fills 40 liters of water in the tank in 8 hours.

 Fills in 1 hour = 40/8 = 5 liters

 4) (A+B) India in 1 hour = 8+5

 = 13 liters

 5) (A+B) fills 40 liters of water

 = 40/13

 = 3.07 hours


 Q.2) Pipe A fills a tank in 8 hours.  But because of the hole it fills in 10 hours.  In how much time can the hole empty this completely filled tank?

 Solution:- In these type of questions,

 1) We have to assume :- The pipe fills 1 liter of water in 1 hour is .

 2) Will fill 8 liters of water in 8 hours.  Hence the capacity of the tank = 8 liters

 3) The pipe pours water into the tank continuously for 10 hours.  Therefore, in 10 hours, a total of 10 liters of water was poured.  Since the tank is out of a total of 8 liters could be water, so the hole is wasted 10 liters to 2 liters of water entered the pipe in 10 hours.

 4) The hole takes 10 hours to empty 2 liters of water.

 Time taken to empty 1 liter

 = 10/2

 = 5 hours

 Time taken to empty 8 liters

 = 8×5

 = 40 hours ans.


 Q.3) Pipe A fills a tank in 4 hours.  Pipe B empties the tank in 8 hours.  How long will it take to fill the pipe if both are opened together?

 Solution:-  T = {(xy)÷(y-x)}

 = {(4×8)÷(8-4)}

 = 32÷4

 = 8 hours ans.


 L.C.M Method:-

 1) L.C.M of 4 and 8 = 8 (The tank can fill 8 liters of water.)

 2) A fills in 1 hour = 8/4 = 2 liters

 3) B empties in 1 hour = 8/8 = 1 liter

 4) Fills 2 liters in 1 hour and 1 liter is empty i.e. in 1 hour only 2-1 = 1 liter of water is filled.

 5) Hence it will take 8 hours to fill 8 liters of water.


 Q.4) Pipes A, B and C can fill a cistern in 4 hours, 6 hours and 8 hours respectively.  How long will it take to fill the tank if all the three pipes are opened simultaneously?

 Solution:-  T= {(xyz)÷(xy+yz+zx)}

 = [(4×6×8)÷{(4×6)+(6×8)+(8×2)}]

 = 192÷(24+48+32)

 = 192÷104

 = 1.84 hours ans.


 L.C.M Method :-

 1) L.C.M of 4,6,8 = 24

 2) Dividing 24 by 4,6,8 gives quotient 6,4,3 respectively.

 3) A, B and C together pour (6+4+3)=13 liters of water in 1 hour.

 4) Time taken to pour 24 liters of water

 = 24/13

 = 1.84 hours ans.


 Q.5) Pipes A,B and C can fill a tank in 60,80 and 100 minutes respectively.  Pipes A and B are turned on continuously for 10 minutes. After that A is closed and B and C are turned on for the next 10 minutes. After 20 minutes all the three pipes A, B, and C are on  .  What is the total time taken to fill the tank?

 Solution:-

 L.C.M of 60,80,100 = 1200

 Dividing 1200 by 60,80,100 gives 20,15,12 respectively.

 So A,B and C fill 20,15 and 12 liters of water respectively in 1 minute. Together, they add (20+15+12)=47 liters of water in 1 minute.

 Amount of water filled by A and B in 10 minutes = 10(20+15)=350 liters

 Amount of water filled by B and C in next 10 minutes = 10(15+12) = 270 liters

 So in 20 minutes total (350+270)=620 liters of water were filled. Now out of 1200 liters (1200-620)= 580 liters of water is left to be filled.

 All three pipes together fill 47 liters of water in 1 minute.  Hence, it will take (580÷47) = 12.34 minutes to fill 580 liters of water.

 Total time taken to fill the tank =(10+10+12.34)=32.34 minutes ans.


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