aptitude : : pipes and cistems
 
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   Exercise 2
   Exercise 1
1.
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres per minute.When the tank is full, the inlet is opened and due to the leak the tank is emptied in 8 hours.The capacity of the tank Iitres.
 
A.
5560litrs

B.

2460litrs
C.
4560litrs
D.
5760litrs
   
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Answer: D
Explanation :
The filler tap can fill the tank in (8*6)/(8-6)=24hrs
Capacity of tank=4*60*24=5760litrs






 
2.
Two pipes X andY can fill a cistern in 24 min. and 32 min. respectively.If both the pipes are opened together, then after how much time should Y be closed so that the tank is full in 18 minutes?
 
A.
8mints

B.

5mints
C.
10mints
D.
None of these
   
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Answer: A
Explanation :
Pipe X remains opened throughout for 18mintus.
X fills 18/24=3/4th of the tank in 18mints.
The remaining 1/4th of the tank is filled by Y in
32(1/4) =8mints.
Hence, Y will be closed aftar 8mints.






 
3.
Two taps can separately fill a cistern in I 0 minutes and I 5 minutes respectively and when the waste pipe is open, they can together fill it iri I 8 minutes. The waste pipe can empty the full cistern in  _________ minutes.
 
A.
9mints

B.

6mints
C.
10mints
D.
2mints
   
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Answer: A
Explanation :
Two taps fill the tank in (10*15)/(10+15)=6mints         .............(1)
Two fillers + a leak fill in 18mints(given)                        ..............(2)
leak will empty the tank in from (1) and (2)
(18*6)/(18-6)=9mints






 
4.
A tank can be filled by one tap in 20 min. and by another in 25 min.Both the taps are kept open for 5 min. and then the second is turned off. In how many minutes more will the tank be completely filled?
 
A.
11mints

B.

10mints
C.
20mints
D.
15mints
   
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Answer: A
Explanation :
In 5 mints, both the pipes fill (5/20)+(5/25)=(1/4)+(1/5)=9/20th of the tank.
Now, 1-(9/20)=11/20 is filled by the first tap.
The first tap can fill 11/20th of the tank in 20*(11/20)=11mints






 
5.
A cistern has two taps which fill it in I 2 min and I 5 min respectively.There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in 20 min. How long will the waste pipe take to empty a full cistern?
 
A.
10mints

B.

5mints
C.
6mints
D.
8mints
   
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Answer: D
Explanation :
Two taps fill the tank in (12*15)/(12+15)=6mints       ............(1)
Two fillers + a leak fill in 20mints (given)     ..................(2)
 
leak will empty the tank in
 
    (20*6)/(26-6)=8mints






 
6.
Two taps can separately fill a cistern in I 0 minutes and I 5 minutes respectively and when the waste pipe is open, they can together fill it iri I 8 minutes. The waste pipe can empty the full cistern in  _________ minutes.
 
A.
9mints

B.

6mints
C.
10mints
D.
2mints
   
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Answer: A
Explanation :
Two taps fill the tank in (10*15)/(10+15)=6mints         .............(1)
Two fillers + a leak fill in 18mints(given)                        ..............(2)
leak will empty the tank in from (1) and (2)
(18*6)/(18-6)=9mints






 
7.
Two taps can separately fill a cistern in I 0 minutes and I 5 minutes respectively and when the waste pipe is open, they can together fill it iri I 8 minutes. The waste pipe can empty the full cistern in _________ minutes.
 
A.
9mints

B.

6mints
C.
10mints
D.
2mints
   
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Answer: A
Explanation :
Two taps fill the tank in (10*15)/(10+15)=6mints         .............(1)
Two fillers + a leak fill in 18mints(given)                        ..............(2)
leak will empty the tank in from (1) and (2)
(18*6)/(18-6)=9mints






 
8.
A cistern has a leak which would empty it in 8 hours. A tap is turned on which admits 6 Jitres a minute into the cistern, and itis now emptied in I 2 hours. How many litres does the cistern hold?
 
A.
8640litrs

B.

7650litrs
C.
5612litrs
D.
None of these
   
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Answer: A
Explanation :
The filler tap can fill the tank in (12*8)/(12-8)=24hrs.
Capacity of tank=6*60*24=8640litrs.






 
9.
Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and A and B can fillit in 7 hours. The time taken by C alone to fill the cistern is
 
A.
10hrs

B.

5hrs
C.
14hrs
D.
1hr
   
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Answer: C
Explanation :
A+B+C can fill a cistern in 6hrs.    ..............(1)
A+B+C can fill 1/3 of cistern in 2hrs.
Now, 1-(1/3)=2/3 of cistern is filled up by A+B in 7hrs.
 
from (1) and (2), C can fill the cistern in
                    (6*(21/2))/((21/2)-6)=(6*21)/9=14hrs






 
10.
Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and A and B can fillit in 7 hours. The time taken by C alone to fill the cistern is
 
A.
10hrs

B.

5hrs
C.
14hrs
D.
1hr
   
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Answer: C
Explanation :
A+B+C can fill a cistern in 6hrs.    ..............(1)
A+B+C can fill 1/3 of cistern in 2hrs.
Now, 1-(1/3)=2/3 of cistern is filled up by A+B in 7hrs.
A+B fill up the cistern in (7*3)/2=21/2hrs.   ................(2)
 
from (1) and (2), C can fill the cistern in
                    (6*(21/2))/((21/2)-6)=(6*21)/9=14hrs
 






 

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