Question

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
A) Only A is sufficient
B) Only B is sufficient
C) Both (A) and (B) are sufficient
D) None

Answer 1

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

A) Only A is sufficient
B) Only B is sufficient
C) Both (A) and (B) are sufficient
D) None

Answer:   C) Both (A) and (B) are sufficient 

Read Description:

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.

Answer 2

Answer:

The correct option is C.

Explanation:

• We know that Pipe A can fill the tank in 40 hours based on assertion A. However, since we lack the data for Pipe B, this information is insufficient. Therefore, statement A by itself cannot provide a response to the query.
• We can infer from statement B that pipe B is only one-third as effective as pipe A. The rate at which Pipe A fills the tank is unknown, though. As a result, we won't be able to determine how quickly Pipe B fills the cistern. As a result, statement B by itself is insufficient to resolve the query.
• When we add up the two claims, we can see that it will take Pipe A 40 hours to fill the cistern.
• The cistern must be filled in 120 hours using Pipe B.
• If they had operated alternately, the cycle might have been initiated by either Pipe A or Pipe B.
• If Pipe A had initiated the filling process, then after two hours, the two pipes would have combined to fill 1/40 + 1/120 = 1/30 th of the tank. or in 30 hours the cistern will be full.
• If Pipe B had initiated the process, then after two hours, the two pipes would have combined to fill 1/120 + 1/40 = 1/30 th of the tank. or in 30 hours the cistern will be full.

The correct response is C because the result is the same no matter which pipe started the sequence.

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