Q:
How long will it take for two pipes A and B to fill an empty cistern if they worked alternately for an hour each ?
A. Working alone, Pipe A can fill the cistern in 40 hours
B. Pipe B is one third as efficient as Pipe A
Answer & Explanation
Answer: C) Both (A) and (B) are sufficient
Explanation: From statement A, we know that Pipe A can fill the tank in 40 hours. However, this information is not sufficient as we do not have the data for Pipe B. Hence, statement A alone cannot answer the given question.
From statement B, we know that Pipe B is one third as efficient as pipe A. However, we do not know the rate at which Pipe A fills the tank. Hence, we will not be able to find the rate at which Pipe B fills the cistern. Therefore, statement B alone is not sufficient to answer the question.
Now, if we combine the two statements, we know that Pipe A take 40 hours to fill the cistern.
Pipe B takes 120 hours to fill the cistern.
If they worked alternately, then either Pipe A could have started the cycle or Pipe B could have started the cycle.
If Pipe A started the sequence of filling alternately, then at the end of two hours, the two pipes together would have filled 1/40 + 1/120 = 1/30 th of the tank in an hour. Or the cistern will fill in 30 hours.
If Pipe B started the sequence, then at the end of 2 hours, the two pipes together would have filled 1/120 + 1/40 = 1/30 th of the tank in an hour. Or the cistern will fill in 30 hours.
As the answer obtained irrespective of which pipe started the sequence is the same, the correct answer is (3) - i.e., both the statement are sufficient to answer the question.
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