Pipes and Cistern

Sponsor Area

Question
SSCCGLENQA12042842

A cistern has 3 pipes A, B and C. A and B can fill it in 3 and 4 hours respectively, and C can empty it in 1 hour. If the pipes are opened at 3 p.m., 4 p.m. and 5 p.m. respectively on the same day, the cistern will be empty at

  • 7 : 12 p.m.

  • 7 : 15 p.m.

  • 7 : 10 p.m.

  • 7 : 18 p.m.

Solution

A.

7 : 12 p.m.

Part of the cistern filled by A in 2 hours i.e. till 5 p.m. 
 equals space 1 third cross times 2 space equals space 2 over 3
Part of the cistern filled by B in 1 hour i.e. till 5 p.m.
equals space 1 fourth
When all three pipes are opened, net part filled in one hour
equals space 1 third plus 1 fourth minus 1 space equals space fraction numerator 4 plus 3 minus 12 over denominator 12 end fraction space equals fraction numerator negative 5 over denominator 12 end fraction
i.e. 5 over 12 part is emptied per hour.
∴ Time taken to empty 11 over 12 space part
      equals space 11 over 12 cross times 12 over 5 space equals space 11 over 5 space hours
equals space 2 space hours space 12 space minutes
∴  Required time = 5 + 2 : 12 = 7 : 12 p.m.

Sponsor Area

Question
SSCCGLENQA12042338

A electric pump can fill a tank in 2 hours. Because of a leak in the tank, it was taking 2 1 half space hours to fill the tank. The leak can drain all the water off the tank in how many hours?

  • 9 hours

  • 10 hours

  • 10 1 half space hours
  • 11 1 half space hours

Solution

B.

10 hours

Let the leak can drain all the water off the tank  = x hours
According to the question,
            1 half minus 1 over straight x space equals space 2 over 5
rightwards double arrow        1 over straight x space equals 1 half minus 2 over 5 space equals fraction numerator 5 minus 4 over denominator 10 end fraction
rightwards double arrow        1 over straight x space equals space 1 over 10
rightwards double arrow        x = 10 hours    

Question
SSCCGLENQA12043030

A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously can empty the pool in half the time that C, the 3rd pipe alone takes to empty it. Pipe A, working alone, takes to empty it. Pipe A, working alone, takes half the time taken by pipe B. Together they take 6 hours 40 minutes to empty the pool. Time taken by pipe A to empty the pool, in hours, is

  • 15

  • 10

  • 30

  • 17

Solution

A.

15

Let the time taken by pipe B to empty the tank  = 2x hours
∴    Time taken by pipe A to empty the tank = x hours
(A and B) takes half of the time that c takes.
∴   Time taken by pipe C
     equals space space fraction numerator 2 over denominator begin display style fraction numerator 1 over denominator 2 straight x end fraction end style plus begin display style 1 over straight x end style end fraction space equals space fraction numerator 2 over denominator begin display style fraction numerator 1 plus 2 over denominator 2 straight x end fraction end style end fraction space equals space fraction numerator 4 straight x over denominator 3 end fraction space hours
A, B and C together take 6 hours 40 minutes
therefore space space space space space 1 over straight x space plus space fraction numerator 1 over denominator 2 straight x end fraction space plus space fraction numerator 3 over denominator 4 straight x end fraction space equals space fraction numerator 1 over denominator 6 plus begin display style 40 over 60 end style end fraction space equals space fraction numerator 1 over denominator 6 plus begin display style 2 over 3 end style end fraction
rightwards double arrow space space space space space fraction numerator 4 plus 2 plus 3 over denominator 4 straight x end fraction space equals space 3 over 20
rightwards double arrow space space space space space 9 space cross times space 20 space equals space 4 straight x space cross times space 3
rightwards double arrow space space space space space space straight x space equals space fraction numerator 9 space cross times space 20 over denominator 4 space cross times space 3 end fraction space equals space 15 space hours

 

Question
SSCCGLENQA12042974

A tank can be filled by pipe A in 2 hours and pipe B in 6 hours. At 10 A.M. pipe A was opened. At what time will the tank be filled if pipe B is opened at 11 A.M.?

  • 12.45 A.M.

  • 5 P.M.

  • 11.45 A.M.

  • 12 P.M.

Solution

C.

11.45 A.M.

Part filled by A in 1 hour  (i.e. till 11 A.M.) = 1 half
Part filled by A and B  in 1 hour (60 minutes):
equals space 1 half plus 1 over 6 space equals space fraction numerator 3 plus 1 over denominator 6 end fraction space equals space 2 over 3
Time taken by A and B to fill 1 half part
                     equals space fraction numerator 60 space cross times space 3 over denominator 2 end fraction space cross times space 1 half
equals space 45 space minutes
∴ Tank will be filled at 11.45 A.M.
        

Question
SSCCGLENQA12042598

A tank has two pipes. The first and pipe can fill it in 4 hours and the second can empty it in 16 hours. If two pipes be opened together at a time, then the tank will be filled in

  • 5 1 half hours
  • 10 hours

  • 6 hours

  • 5 1 third space hours

Solution

D.

5 1 third space hours

Part of tank filled by both the pipes in 1 hour
    equals space 1 fourth minus 1 over 16 space equals space fraction numerator 4 minus 1 over denominator 16 end fraction space equals space 3 over 16
∴   Required time = 16 over 3