Problems on Pipes and Cistern Part 2

Problems on Pipes and Cistern Part 2


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.
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
Answer: Option E
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
91090
 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.
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
Answer: Option E
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
81616
 Tank will be emptied in 16 minutes.
Thus, both I and II are necessary to answer the question.
 Correct answer is (E).
3. 
If both the pipes are opened, how many hours will be taken to fill the tank?
I. 
The capacity of the tank is 400 litres.
II. 
The pipe A fills the tank in 4 hours.
 III. 
The pipe B fills the tank in 6 hours.
A.Only I and II
B.Only II and III
C.All I, II and III
D.Any two of the three
E.Even with all the three statements, answer cannot be given.
Answer: Option B
Explanation:
  II. Part of the tank filled by A in 1 hour =1
4
III. Part of the tank filled by B in 1 hour =1
6
(A + B)'s 1 hour's work =1+1=5
4612
 A and B will fill the tank in12hrs = 2 hrs 24 min.
5
So, II and III are needed.
 Correct answer is (B).

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