If 8 men and 6 boys can dig a well in 2 days, and 6 men and 2 boys can do it in 3 days, how long will 5 men and 3 boys take to do it?

a)4.33
b)4
c)3
d)3.33

• Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
  so 8x+6y=1/2,& 6x+2y=1/3 on solving these two equation we get x=1/20 and y=1/60 days..5 men(x)+3 boy(y) 1 days work =(5/20+3/60)=3/10
  so they will complete the work in 3.33 days..
  
• 12 years agoHelpfull: Yes(4) No(0)
• 1 man can dig a well in = x days
  
  1 boy can dig a well in = y days.
  
  work done by a man in 1 day= days
  
  work done by 1a boy in 1 day = days
  
  Total work done by 8 men and 6 boys :-
  
  ( + ) = .. (1)
  
  Total work done by 6 men and 2 boys :-
  
  ( + )= .. (2)
  
  By multiplying equation (2) with 3, we get:-
  
  + = = 1.. ( 3)
  
  now (1) -(3) :-
  
  + =
  
  + = 1
  
  - - -
  
  ------------
  
  - = - 1 = -
  
  = -
  
  - = -
  
  x = 20
  
  putting the value of x in equation (1) , we get :-
  
  ( + ) =
  
  + =
  
  = - = = =
  
  ∴ y = 6 × 10 = 60
  
  1 man can dig the well in = 20 days
  
  ∴1 man can do the work in 1 day = part
  
  ∴ 5 men can dig a well in = × 5 = 4 days.
  
  1 boy can dig the well in = 60 days
  
  ∴ 1 boy can do in 1 day = part
  
  ∴3 boys can dig a well in = × 3 = 20 days
  
  Total work done in 1 day = + = = =
  
  hence 5 men and 3 boys take to do it in 15 days.
  
  Ans :- 5 men and 3 boys take to do it in 15 days.
• 6 Months agoHelpfull: Yes(0) No(0)