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Aptitude - Pipes and Cistern

Exercise : Pipes and Cistern - Data Sufficiency 1
Directions to Solve

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

  • Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
  • Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
  • Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
  • Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
  • Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
1.

How much time will the leak take to empty the full cistern?

I. 

The cistern is normally filled in 9 hours.

 II. 

It takes one hour more than the usual time to fill the cistern because of la leak in the bottom.

I alone sufficient while II alone not sufficient to answer
II alone sufficient while I alone not sufficient to answer
Either I or II alone sufficient to answer
Both I and II are not sufficient to answer
Both I and II are necessary to answer
Answer: Option
Explanation:

 I. Time taken to fill the cistern without leak = 9 hours.

Part of cistern filled without leak in 1 hour = 1
9

II. Time taken to fill the cistern in presence of leak = 10 hours.

Net filling in 1 hour = 1
10

Work done by leak in 1 hour = 1 - 1 = 1
9 10 90

Leak will empty the full cistern in 90 hours.

Clearly, both I and II are necessary to answer the question.

Correct answer is (E).

2.

How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B are opened simultaneously?

I. 

A can fill the tank in 16 minutes.

 II. 

B can empty the full tank in 8 minutes.

I alone sufficient while II alone not sufficient to answer
II alone sufficient while I alone not sufficient to answer
Either I or II alone sufficient to answer
Both I and II are not sufficient to answer
Both I and II are necessary to answer
Answer: Option
Explanation:

 I. A's 1 minute's filling work = 1
16

II. B's 1 minute's filling work = 1
8

(A + B)'s 1 minute's emptying work = 1 - 1 = 1
8 16 16

Tank will be emptied in 16 minutes.

Thus, both I and II are necessary to answer the question.

Correct answer is (E).

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