Tuesday, 24 January 2017

Shortcuts for Pipes, Cistern,Tank Problems

Pipes And Cisterns Shortcut Methods

Pipes And Cisterns Shortcut Methods

Pipe and Cistern problems are very important for exams like SSC, Bank, railway etc.
we have compiled some shortcuts for the problems of pipe and cistern. you may check  them below

What is pipe

A pipe is used to fill or empty the tank or cistern.

Types of pipes-

1-Inlet Pipe: A pipe connected to the tanks and used to fill the tank or cistern is known as Inlet Pipe.

2-Outlet Pipe: A pipe  connected to the tank and used to empty the tank or cistern is known as Outlet Pipe.

Basic Formulas of Pipes and Cisterns

  1. If an pipe fill the tank in x hours, then the part filled in 1 hour = 1/x
  2. If an outlet pipe can vacant the tank in y hours, then the part that will be empty in 1 hour = 1/y
  3. If both inlet pipe and outlet pipe are kept open, then the net part of the tank filled in 1 hour is

Examples for Shortcut Methods for Pipes and Cisterns

Q1. Two pipes A&B can fill a tank in 48 min. and 36 min. . if both pipes are opened together then after how much time pipe A should be closed so that the whole tank fill in 25 min 30 sec.

sol.  A can fill the tank -- 48 min.
       B can fill the tank -- 36 min

        step 1 -    now take L.C.M 
                          L.C.M = 144
        step 2 -     A's part = 144/48 = 3
                         B's part = 144/36 = 4

                          if A closed then b will fill remaining tank then
                           B~ 51/2 min. (25 min. 30 sec.)

        step 3 -       multiply it with B's part
                            (51/2)x4  =  102

                   subtract 102 from 144 and divide the result by A's part thats the ans
                       42/3 = 14 min.  

Q2. Two intel pipes  A&B can fill a tank in 12 min. and 16 min. respectively. both intel pipes are opened together but 4 min. before the cistern is full, pipe A is closed. how much time will the tank take to fill.

sol.  A can fill the tank -- 12 min.
       B can fill the tank -- 16 min

        step 1 -    now take L.C.M 
                          L.C.M = 48
        step 2 -     A's part = 48/12 = 4
                         B's part = 48/16 = 3

        step 3 -       if only b fill tank in last 4 min. then it will fill  4x3 = 12 unit
                         subtract 12 from 48  (total work - B's work done alone) = 36
                        in 36 min, both A and B done the work so Combined part of A and B will                          be = 4+3 =7
        step 4 -    (36/7)+4= 64/7 min.

                                        shortcut method 

           48+16 = 64

Q3.         Two pipes A and b can fill a tank in 1 hour and 75 minutes respectively. There is also an outlet pipe C. If all the three pipes are opened together, the tank is full in 50 minutes. How much time will be taken by C to empty the full tank.

sol.      A can fill the tank -- 60 min.
       B can fill the tank -- 75 min
        C is outlet pipe so we use - sign before it.
         if all pipes are opened together the then tank full in 50 min then A+B-c = 50

        step 1 -    now take L.C.M of all three
                          L.C.M = 300
        step 2 -     A's part = 300/60 = 5
                         B's part = 300/75 =  4
                         A+b-C's part = 300/50 = 6

                          we know A+B = 9 and A+B-C =6 then C= 3
                           c will empty tank in 300/3 = 100 min.

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