2 pipes A & B can fill a cistern in 12 min and 16 min resp. If both pipes are opend together then after hw mch time B shld be closed so tht the tank is full in 9 min
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,554 answers
starTop subjects are Math, Science, and Business
Pipe A fills the tank in 12 minutes. In a minute 1/12 of the tank is filled. Similarly for tank B, in a minute 1/16 of the tank is filled.
When both the pipes are opened to fill the tank, let the time for which the pipe B is closed to fill the tank in 9 minutes be T.
This gives 9*(1/12) + (9 - T)*(1/16) = 1
=> 9/12 + 9/16 - T/16 = 1
=> T/16 = 9/12 + 9/16 - 1
=> T/16 = 5/16
=> T = 5
Therefore the pipe B should be kept close for 5 minutes.
Related Questions
- Two pipes fill a storage tank in 9 hours. The smaller pipe takes 3 times as long to fill the...
- 1 Educator Answer
- A tank can be fully filled with water using a pipe that fills 20 liters in a minute. A bigger...
- 2 Educator Answers
- A tank can be filled in 4 hours using pipe A and emptied in 2 hours using pipe B. How much is the...
- 1 Educator Answer
- 2 taps A and B can fill a bucket in 12 and 18 minutes resp. How long will it take both the taps...
- 2 Educator Answers
- If both are used together, how long will it take to fill the empty tanker of an oil tanker that...
- 2 Educator Answers
A alone can fill 1/12 of the cistern in 1 minute.
B alone can fill (1/16)th of the cistern.
Let the pipes work together for x minutes to fill the empty cistern
So in x minutes (1/12+1/16)x = 7x/48 of the cistern is filled up.
If B is closed at the xth minute, then the rest of the tank to be filled up by A alone = 1- 7x/48 = (48-7x)/48.
(49-7x)/48 of the cistern can be filled by A in {(48-7x)/48}/(1/12) minutes
Therefore x+ {(48-7x)/48}/(1/12) = 9 minutes
=> x+(48-7x)/4 = 9
=>4x +(48-7x) = 9*4
=> 4x+48-7x = 36
=> 48-36 = 7x-4x
=> 12 = 3x
=> x = 12/3 hrs = 4 mins.
Therefore, B should be closed after 4 minutes so that the pipe A can fill the cistern is full in the 9 minutes.
Student Answers