4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work?

1) 22(2/7) days
2) 25(1/2) days
3) 5(1/7) days
4) 12(7/22) days

• M1D1=M2D2
  
  (4M+3W)6=(5M+7W)4
  24M+18W = 20M + 28W
  4M=10W
  2M=5W
  ratio of M:W = 5:2
  To find work put 5:2 in one of the side of equation
  WD= (4*5+3*2)6 = 156
  for 1W & 1M
  Time = WD/there capacity
  =156/(5+2)
  = 156/7
  = 22(2/7) =(a)
• 9 years agoHelpfull: Yes(1) No(0)
• Let 1 man's 1 day work = x and 1 woman's 1 day work = y.
  
  Hence, 4x + 3y = 1/6 ……i
  
  and 5x + 7y = 1/4 ………ii
  
  By solving i & ii we get y = 1/78 and x = 5/156.
  
  Now x + y = 5/156 + 1/78 = 7/156
  
  So 1 man's and I woman's 1 day work= 7/156 part. So they will finish the whole work = 1÷ 7/156 = 1*156/7 = 22 2/7 days.
• 1 year agoHelpfull: Yes(0) No(0)