3. A work can be done by 8 men and 10 women in 25 days, the same work can be done by 10 children and 5 women. In how many days 2 children and 3 men finish the work?

• 8x+10y=1/25............(1)
  10z+5y=1/25..............(2) multiply by 2 in eq 2 then 20z+10y=2/25...........(3)
  solve it eq(1) and eq(2)
  we got 92 days
• 10 years agoHelpfull: Yes(4) No(8)
• explain it please
• 10 years agoHelpfull: Yes(2) No(1)
• ~92 days......
  http://www.beatthegmat.com/work-can-be-done-by-8-men-and-10-women-in-25-days-t70368.html
• 10 years agoHelpfull: Yes(1) No(12)
• Here we could formulate only two equations with three variables. For the number of variables exceeding the number of equations we must assign parameter to the third variable. Depending on the type of parameter used, we attain various degrees of a precision for the represented values. Let's start
  
  x= men
  y=women
  z=children
  
  one-day work - men and women, 8x+10y=1/25 Equation (1); children and women, 10z+5y=1/25 Equation (2)
  
  Take 2 times the Equation (2), 20z+10y=2/25
  then, subtract Equation (1) from Equation (2) after multiplication
  20z+10y - 8x-10y = 2/25-1/25
  20z-8x=1/25, 500z-200x=1
  
  Work completed is equal to (500z-200x) or 1
  
  Time required for the completion of work by children and men (2z+3x)
  (500z-200x)/(2z+3x)=Time (if not integer, add [+] 0.5)
  
  To find time, we must assign the parametric condition to a denominator (2z+3x) which must Not Be equal (=) to 0.
  It can not be negative too, since the work pieces completed by children (z) and men (x) are positive values. Hence, we formulate the inequality |2z| + |3x| > 0
  
  Let's solve the system of equation and one inequality for now:
  { 500z-200x=1
  { |2z| + |3x| > 0
  
  We must consider only z>0 and x>0 (see the parametric conditions above)
  {500z-200x=1
  {2z => 3x
  {3x => 2z
  
  let's focus on 2z=3x, since this condition is present in both inequalities z=3x/2
  
  500*(3x/2)-200x=1, 750x-200x=1, 550x=1, x=1/550
  z=3/(550*2)=3/1100
  
  Now plug in the values for x (1/550) and z (3/1100)
  3x+2z, 3*(1/550)+2*(3/1100) = 3/550+6/1100 = (6+6)/1100 = 12/1100 = 3/275
  
  The work completed is equal to 500z-200x=1
  Time=Work completed/(3x+2z), 1/(3/275)=275/3
  
  2 children and 3 men should complete the work at 275/3 (@ if not integer, add [+] 0.5) 275/3+1/2=553/6 ~ 92 days
  
  I bet your answer is different. It's natural, since we have three variables and only two defined equations.
• 6 years agoHelpfull: Yes(1) No(3)