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

• B will take 30 days
  First of all,
  (1/x)+(1/y)=1/7.5
  and (x/2)+(y/2)=20
  On solving,x=10,y=30
  So,A tajes 10 days and B takes 30 days to complete the work
• 12 years agoHelpfull: Yes(25) No(2)
• 
  Solution
  A will complete (1/a) th of the job in a day.
  B will complete (1/b) th of the job in a day.
  A and B will complete the job in 7.5 or (15/2) days
  (1/a) + (1/b) = 1 /(15/2)
  (1/a) + (1/b) = 2/15 .......>1Eqn
  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.
  A can complete the job working alone in 'a' days,
  so a/2 days
  B will complete the remaining half of the job in days
  so b/2 days
  a/2 + b/2 =20
  ==> a+b=40 ==> a=40–b .....>2Eqn
  sub eqn(2) in Eqn(1) we get
  (1/40−b) + (1/b) = 2/15
  (b + 40 - b)/ b(40-b) = 2/15
  40/(40b-b^2) = 2 /15
  600 = 80b- 2b^2
  40-b^2 = 300 (Sub by 2)
  B^2 - 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.
  
• 10 years agoHelpfull: Yes(6) No(1)
• Let the total Work be 7.5
  so, A+B unit time work= 1
  
  Let A worked for x days then as per the question
  
  (7.5/2)/x + (7.5/2)/(20-x)=1
  (7.5/2)20=x(20-x)
  x^2-20x+75=0
  x=5,15
  Since A more efficient so, B will take 15 days to complete half work or 30 days for whole work
  30 Ans.
• 6 years agoHelpfull: Yes(1) No(2)