A pipe can fill a cistern in 12 min and another pipe can fill it in 15 min,but a third pipe can empty it in 6 min. the first two pipes are kept open for 5 min in the beginning and then the third pipe is also opened.in what time is the cistern emptied

• 45 min
  
  In 1 min
  1st pipe fills =1/12
  2nd pipe fills =1/15
  
  In 1st 5 min
  fraction of cistern filled = 5/12 + 5/15
  =(25+20)/60
  =45/60
  =3/4
  
  Since the 3 pipes are opened after 5 mins,
  fraction emptied in 1 min = 1/6 - (1/12 + 1/15)
  =(10-5+4)/60
  =1/60
  
  ===>60 min to empty fully filled cistern
  Since the cistern is 3/4 filled
  
  Time taken to empty = 60*3/4
  =45 minutes
• 10 years agoHelpfull: Yes(4) No(0)
• 5(1/12 + 1/15 )=45/60
  remaining work there for is 1 - 45/60=15/60
  let the time taken be x hrs.
  x(1/6 - 1/12 + 1/15 )=3/4
  x=45 mins
  so it takes 45 mins to empty the tank
• 9 years agoHelpfull: Yes(2) No(0)
• the filled part is 5(1/12 + 1/15)=3/4
  let X be time taken to empty the tank..
  so,
  X(1/6)=3/4
  X=9/2 mins...
  X=4mins 30 secs...
• 9 years agoHelpfull: Yes(0) No(1)
• let the tank be of 60 L (Lcm of 14 & 15)
  1st pipe will fill=60/12=5 L per min
  & 2nd pipe will fill=60/15=4 L per min
  1+2 pipe will fill=(5+4) 9 L per min
  since 1 & 2 are opened for 1st 5 min ,
  then tank filled=9*5=45 L
  
  3rd can empty=60/6=10 L per min
  
  when third pipe is opened
  
  1+2+3 pipe will fill=5+4-10= -1 L per min
  that means will emty 1 L per min.
  
  so 45/1=45 min will be taken to emty the tank
  
• 8 years agoHelpfull: Yes(0) No(0)
• A(fill)->12min
  b(fill)->15min
  c(empty)->6min
  lcm(15,10,6)=60unit ->total work
  A->60/12->5unit/min,B->60/15->4unit/min,C->60/6->10unit/min
  A+B=9unit /min in 5min=45unit water fill
  A+B+c=5+4-10=-1unit/min
  so,empty in 45 min
  
• 8 years agoHelpfull: Yes(0) No(0)
• when all 3 pipes will be open it will take time = 45min
  Soln:
  time by first pipe= 12min
  time by 2nd pipe=15min
  time taken by 3rd pipe to empty=6min
  work done by 1st pipe(per min ) = 1/12
  work done by 2nd pipe(per min)= 1/15
  work done by 3rd pipe(per min)= 1/6
  work done by 1st&2nd pipes in min=(1/15+1/12)
  = 3/20
  work done by them in 5 min= 3/4
  when all pipes are open cistern drained in min=1/60
  time to drain 3/4 of cistern =45min
  
• 7 years agoHelpfull: Yes(0) No(0)