8. A contractor has divided his labourers into class A & B. 7 class A lobourers & 5 class B labourers finish a piece of work in 2 days while 2 class A labourers & 3 class B labourers finish the same work in 5 days. In how much time would 3 class A & 10 class B labourers finish the same work?

• (7A+5B) do in 1 day 1/2 unit so (14A+10B) do in 1 day 1 unit...(1) & (21A+15B) do in 1 day 3/2 unit....(2)
  (2A+3B) do in 1 day 1/5 unit so (14A+21B) do in 1 day 7/5 unit...(3) & (10A+15B) do in 1 day 1 unit...(4)
  performing (3)-(1) & (2)-(4) we get B & A do in 1 day 2/55 & 1/22 unit respectively so (10B+3A) do in 1 day (2/55*10+1/22*3)=1/2 unit
  therefore the whole work will be done by them in 2 days
  
• 11 years agoHelpfull: Yes(17) No(3)
• 7a+5b=1/2...eqn1
  2a+3b=1/5...eqn2
  solve 1 and 2
  get b=2/55 and a=1/22
  3a+10b=1/2 so ans is 2days
• 11 years agoHelpfull: Yes(4) No(0)
• let amount of work done by A in one day=x and B=y
  so, 2(7x+5y)= 5(2x+3y)
  which boils down to x=5/4y
  so in terms of y total work done can be calculated by putting
  in one of above equation and it comes out to be 110y/4
  Now creating last required equation in terms of y,
  we will get-> n(3*5/4y+ 10y)= 110y/4
  solving it and n, number of day come out to be 2,Ans-2
• 11 years agoHelpfull: Yes(0) No(2)
• in 2 days=ans
• 11 years agoHelpfull: Yes(0) No(0)
• ans is 2 days ..
  
• 11 years agoHelpfull: Yes(0) No(0)