Aptitude - Pipes and Cistern
1.
Two pipes can fill a tank in 20 minutes and 30 minutes respectively. If both the pipes are opened simultaneously, then the tank will be filled in
Answer
Part filled by both pipes in 1 min =
120 + 130 
= 560 = 112
Time taken to fill the tank = 12 minutes.
Answer :
Option BExplanation :
Part filled by both pipes in 1 min =
120 + 130 = 560 = 112Time taken to fill the tank = 12 minutes.
2.
A pipe can empty a tank in 40 minutes. A second pipe with diameter twice as much that of the first is also attached with the tank to empty it. The two together can empty the tank in
Answer
A pipe with double the diameter will take half-time.
So, the second pipe can empty the full tank in 20 min.
Part emptied by both in 1 min = 140 + 120 = 340
Time taken to empty the full tank = 403 min ≈ 13.33 min
Answer :
Option BExplanation :
A pipe with double the diameter will take half-time.
So, the second pipe can empty the full tank in 20 min.
Part emptied by both in 1 min =
140 + 120 = 340Time taken to empty the full tank = 403 min ≈ 13.33 min
3.
Two pipes can fill a tank in 15 hours and 12 hours respectively and a third pipe can empty it in 4 hours. If the pipes be opened in order at 8 A.M., 9 A.M. and 11 A.M. respectively, the tank will be emptied at
Answer
Let the tank be emptied in x hrs after 8 A.M.
Work done by A in x hrs, by B in (x − 1)hrs and by C in (x − 3)hrs = 0
⇒ x15 + (x − 1)12 − (x − 3)4 = 0
⇒ 4x + 5(x − 1) − 15(x − 3) = 0
⇒ 6x = 40 ⇒ x = 203hrs
⇒ x = 6 hrs 40 min after after 8 A.M.
Hence, the tank will be emptied at 14 hrs 40 min, i.e. 2:40 P.M.
Answer :
Option DExplanation :
Let the tank be emptied in x hrs after 8 A.M.
Work done by A in x hrs, by B in (x − 1)hrs and by C in (x − 3)hrs = 0
⇒ x15 + (x − 1)12 − (x − 3)4 = 0
⇒ 4x + 5(x − 1) − 15(x − 3) = 0
⇒ 6x = 40 ⇒ x = 203hrs
⇒ x = 6 hrs 40 min after after 8 A.M.
Hence, the tank will be emptied at 14 hrs 40 min, i.e. 2:40 P.M.
4.
A cistern has a leak which could empty it in 8 hrs. A tap is turned on which admits 6 litres a minute into the cistern and it is now emptied in 12 hrs. How many litres does the cistern hold ?
Answer
Part filled in 1 hour = 18 − 112 = 124
Time taken to fill the cistern = 24 hrs.
Water moved in it in 24 hrs = (6 x 60 x 24) litres = 8640 litres
Capacity of the cistern = 8640 litres.
Answer :
Option DExplanation :
Part filled in 1 hour =
18 − 112 = 124Time taken to fill the cistern = 24 hrs.
Water moved in it in 24 hrs = (6 x 60 x 24) litres = 8640 litres
Capacity of the cistern = 8640 litres.
5.
A pipe can fill a tank in x hrs and another pipe can empty it in y(y > x) hrs. If both the pipes are open, in how many hours will the tank be filled ?
Answer
Part filled by both pipes in 1 hr = 1x − 1y = (y − x)xy
∴ The tank will be filled in xy(y − x) hours
Answer :
Option DExplanation :
Part filled by both pipes in 1 hr =
1x − 1y = (y − x)xy∴ The tank will be filled in xy(y − x) hours
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