A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?20 hours25 hours35 hoursCannot be determinedNone of these
Question
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?20 hours25 hours35 hoursCannot be determinedNone of these
Solution
Let's denote the rate at which pipe A fills the tank as 'a', the rate for pipe B as 'b', and the rate for pipe C as 'c'.
From the problem, we know that pipe C is twice as fast as B and B is twice as fast as A. So we can write these relationships as:
b = 2a c = 2b = 4a
We also know that all three pipes together can fill the tank in 5 hours. So, the sum of their rates equals the reciprocal of this time:
a + b + c = 1/5
Substituting the relationships we found earlier into this equation gives:
a + 2a + 4a = 1/5 7a = 1/5 a = 1/35
So, pipe A alone would take 35 hours to fill the tank. Therefore, the answer is 35 hours.
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