A and B can do a piece of work in 21 and 24 days respectively. They started the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?

• In 9 days B completes 9/24 i.e., 3/8th of the work.
  
  Hence 1 - 3/8 = 5/8th of the work is completed by A and B together.
  
  i.e., x (1/21 + 1/24) = 5/8 => x = 7 days.
• 12 years agoHelpfull: Yes(25) No(11)
• 1/24*9*21=7.875 days
• 11 years agoHelpfull: Yes(1) No(6)
• x/21+x/24=5x/56
  remaining work=(51-5x)/56=9/24(work done by b in 9 days)
  x=7
• 11 years agoHelpfull: Yes(1) No(0)
• for example : A’s one day’s work = 1/45
  B’s one day’s work = 1/40
  ∴
  (A+B)’s 1day’s work
  =
  45
  1
  +
  40
  1
  (take LCM)
  =
  360
  9
  8
  +
  =
  360
  17
  Work done by B in k23 days = 1/40 x 23 = 23/40
  Remaining work = 1 – 23/40 =
  40
  23
  40
  −
  = 17/40
  (A+B)’s 1day’s work
  =
  360
  17
  17/40 work done by (A + B) in 1 x 360/17 x 17/40 = 9 days
• 9 years agoHelpfull: Yes(0) No(0)
• (A+B)'s 1 day work = 1/21+1/24
  = 5/56
  Work done by B in 9 days = 9/24
  = 3/8
  Remaining Work = 5/8
  Thus, 5/8 work was done by (A+B) in 56/5*5/8
  => 7 days
  After 7 days A leaves the work.
• 7 years agoHelpfull: Yes(0) No(0)