Pipes and Cistern - Arithmetic Aptitude Questions and Answers

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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 E

Explanation :

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

Part of cistern filled without leak in 1 hour =\(\frac { 1 } { 9 }\)

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

Net filling in 1 hour =\(\frac { 1 } {10 }\)

Work done by leak in 1 hour =[\(\frac { 1 } { 9 }\)-\(\frac { 1 } {10 }\)]=\(\frac { 1 } {90 }\)

Leak will empty the full cistern in 90 hours.

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

Correct answer is (E).

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