An empty tank is filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled find the time taken to fill the tank?

a. 16
b. 18
c. 20
d. 21

• let the tank be filled in t minutes after opening tap C
  now total part of tank filled=[(t/42)-(t/30)+(t/35)]
  now
  (12/42)-(6/30)+(6/42)+[(t/42)-(t/30)+(t/35)=1
  solve for t we get t=40.5 minutes
  therefore
  total time= 40.5min + 12min(when A was opened) + 6 min(when B was opened)= 58.5 min ans.
  
  
  This is correct Options are wrong
• 10 years agoHelpfull: Yes(21) No(4)
• Pipe A in one minute fills 1/42 of the tank. Pipe A is totally kept open for 12 + 6 -> 18 minutes before Pipe C is opened. Thus in 18 minutes Pipe A fills 18/42 -> 3/7 capacity of the tank.
  
  Pipe B can drain the tank in 30 minutes and in one minute can drain 1/30 of the tank.
  
  Pipe B is kept open for 6 minutes before Pipe C is opened. In this 6 minutes it would have drained 6/30 -> 1/5 capacity of the tank.
  
  Hence, after 18 minutes the tank is filled up to – > 3/7 – 1/5 -> 8/35 capacity.
  
  The remaining capacity to be filled is -> 27/35
  
  All the three pipes are now running to fill this quantity.
  
  Pipe C in one minute can fill 1/35 capacity.
  
  Now in one minute both Pipes A and C fills and C drains. The quantum filled in one
  
  Minute is -> 1/42 + 1/35 – 1/30 -> 2/70.
  
  Thus to fill the remaining capacity of 27/35 the time taken will be 27/35 * 70/2 -> 27 minutes.
  
  Hence, the total time taken to fill the tank is 12 + 6 + 27 = 45 minutes.
• 10 years agoHelpfull: Yes(12) No(2)
• Take lcm of 42,12,35=210. Assume vol tank =210lt. Now tank is filled in 42 min. Tank is emptied for 12 min i.e. 84lt. now tank is filled by c in 84/4=21min
• 10 years agoHelpfull: Yes(1) No(1)
• yghbnhunm lcm is 20
• 10 years agoHelpfull: Yes(0) No(0)
• There is no correct option. ....I think this is dummy question .
• 10 years agoHelpfull: Yes(0) No(0)
• @Miraj: why are we adding A and B's time?
  when total time is coming as 40.5?
• 10 years agoHelpfull: Yes(0) No(0)