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
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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