if A and B work together,they will complete a job in 7.5days.however,if A works alone and completes half the work and then B takes over and completes the remaining half alone,they will take 20days.how long will B alone take to do the work if A is more efficient than B ?

• Let 'a' be the number of days in which A can do the job alone. Therefore, working alone, A will complete 1 by a th of the job in a day.
  
  Similarly, let 'b' be the number of days in which B can do the job alone. Hence, B will complete 1 by bth of the job in a day.
  
  Working together, A and B will complete 1/a + 1/b of the job in a day.
  
  The problem states that working together, A and B will complete the job in 7.5 or 15/2 days. i.e they will complete 2/15th of the job in a day.
  
  Therefore, 1/a + 1/b = 2/15 ...... (1)
  
  From the question, we know that if A completes half the job working alone and B takes over and completes the next half, they will take 20 days.
  
  As A can complete the job working alone in 'a' days, he will complete half the job, working alone, in a/2 days.
  Similarly, B will complete the remaining half of the job in b/2 days.
  Therefore, a/2 + b/2 = 30 => a + b = 40 or a = 40 - b ...... (2)
  
  From (1) and (2) we get, 1/40-b + 1/b = 2/15 => 600 = 2b(40 - b)
  
  => 600 = 80b - 2b2
  => b2 - 40b + 300 = 0
  => (b - 30)(b - 10) = 0
  => b = 30 or b = 10.
  
  If b = 30, then a = 40 - 30 = 10 or
  If b = 10, then a = 40 - 10 = 30.
  
  As A is more efficient than B, he will take lesser time to do the job alone. Hence A will take only 10 days and B will take 30 days.
• 11 years agoHelpfull: Yes(5) No(1)
• let A's 1day's work be 1/x and B's be 1/y
  (1/x)+(1/y)=(1/7.5) (given)
  also given x/2 + y/2=20 ==> x+y=40
  on solving we get x=10 and y=30 (since A is more efficient than B)
  Hence B alone can take 30 days to complete the work
• 11 years agoHelpfull: Yes(3) No(0)
• A and B= 7.5 days (8 units/day)
  Aalone and Balone(for either half)-20 days(3 units/day)
  lcm=60 units
  A=5units B=3 units and A=6units B=3units are possible solutions as A+B=8units
  1 st half
  30units done by A (30/6= 5 days )
  2nd half
  30units done by B (30/2=15 days )
  total=20 days.
  
  therefore, B's work= 60/2 = 30 days
• 11 years agoHelpfull: Yes(1) No(0)