Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both working together. If B worked alone, he would need 4 1/2 hours more to compete the job than they both working together. What time would they take to do the work together.

• let both are complete the work in x hour.
  so, A complete the work in X+8 hour
  B complete the work in X+9/2 hour
  1/(X+8) + 1/(X+9/2) = 1/X
  solve the equetion =2X^2=72
  X^2=36
  X=6.
  so both can complete the work together in 6 days.
• 11 years agoHelpfull: Yes(12) No(0)
• Let T be the number of hours to complete the job working together by A & B
  Then T+8 = number of hours for A to complete the job working alone
  and T+4.5 = number of hours for B to complete the job working alone
  
  In 1 hour, A will complete 1 / ( T + 8 ) of the job
  In 1 hour, B will complete 1 / ( T + 4.5 ) of the job
  In 1 hour, A and B will complete 1 / T of the job
  
  Then
  
  1 / T = 1 / ( T + 8 ) + 1 / ( T + 4.5 ).......................................... ( 1 )
  Then L.C .M = T ( T + 8 ) ( T + 4.5 )
  Multiplying Eq ( 1 ) by the L C M
  ( T + 8 ) ( T + 4.5 ) = T ( T + 4.5 ) + T ( T + 8 )
  T² + 8 T + 4.5 T + 36 = T² + 4.5 T + T² + 8 T
  T² - T² - T² + 8 T + 4.5 T - 8 T - 4.5 T + 36 = 0
  - T² + 36 = 0
  36 = T²
  6 =T = Time taken by both to complete the job = 6 hours
• 9 years agoHelpfull: Yes(2) No(0)
• Let us suppose both take x hours to complete the work
  
  alone
  A takes 8+x
  B takes 9/2+x (by solving 4*1/2)
  
  in 1 day
  A 1/8+x
  B (1/1)/(9/2+x/1) which becomes after solving 2/9+2x
  B is 2/9+2x (1 day)
  both(A+B) will take 1/x
  
  Setting equation
  (1/8+x)+(2/9+2x)=1/x (a+b=1/x) for 1 day
  By applying rule for addition of such expressions on L.H.S.
  
  ((9+2x)(1)+(8+x)(2))/(8+x)(9+2x)=1/x
  
  after solving
  
  (4x+25)/(2x^2(i.e.raised to power of 2)+25x+72)=1/x
  now cross multiply
  
  x(4x+25)=2x^2+25x+72
  solve it
  2x^2=72
  x^2=72/2 that is 36
  x=square root of 36 i.e 6 Answer complete
• 11 years agoHelpfull: Yes(1) No(0)