Math, asked by Eesho, 8 months ago

There are three pipes A, B and C. Pipe B takes 1 hour more than pipe A to fill the tank and pipe C take 12 minutes more than half the time taken by pipe A to fill the same tank. It is one and the same thing to fill the tank by pipes A and B together or to use only pipe C. The total time taken to fill the tank by A, B and C together is:

Answers

Answered by amitnrw
0

Given :  There are three pipes A, B and C. Pipe B takes 1 hour more than pipe A to fill the tank and pipe C take 12 minutes more than half the time taken by pipe A to fill the same tank. It is one and the same thing to fill the tank by pipes A and B together or to use only pipe C.  

To find :  . The total time taken to fill the tank by A, B and C together is:

Solution:

Let say time taken by pipe A to fill the tank   =  A mins

then time taken by Pipe B  to fill  the tank   = A + 60 Mins

time taken by  Pipe  C  to fill  the tank   = A/2 + 12   = (A + 24 )/2  Mins

Tank filled by pipe A & B in 1 Min  = 1/A  + 1/(A + 60)

Tank filled by pipe C in 1 Min  =1 / (A + 24)/2  = 2/(A + 24)  

1/A  + 1/(A + 60)  = 2/(A + 24)

=> (2A + 60)(A + 24) = 2 A(A + 60)

=> (A + 30)(A + 24) = A(A + 60)

=> A² + 54A + 720 = A² + 60A

=> 6A = 720

=> A = 120

Tank filled by pipe A & B in 1 Min =  1/120 + 1/(120 + 60)  =  1/72

Tank filled by pipe C in 1 Min  = 2 /(120 + 24)  = 1/72  

Tank filled by pipe A , B & C  in 1 Min  = 1/72 + 1/72   =  1/36

The total time taken to fill the tank by A, B and C together is:  36 Mins  

36 Minutes is correct Answer

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