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Pipes and Cistern - General Aptitude

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.
Q1:

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.

A I alone sufficient while II alone not sufficient to answer

B II alone sufficient while I alone not sufficient to answer

C Either I or II alone sufficient to answer

D Both I and II are not sufficient to answer

E Both I and II are necessary to answer

ANS:E - Both I and II are necessary to answer

 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).