Three men can do as much work as 5 boys and the wages of 3 boys are equal to those of 2 men. A work on which 40 boys and 15 men are employed takes 8 weeks and costs Rs 15750. How long would it take if 20 boys and 20 men were employed , and how much would it costs?

• around 69 days. Rs 12600
• 10 years agoHelpfull: Yes(15) No(7)
• 3 men work = 5 boys work
  so let work done by 1 boy in 1 day = 1/5;
  then work done by 1 man in 1 day = 1/3;
  so total work done in 8 weeks = work done by boys + work done by men
  = 1/5*40*8*7 +1/3*15*8*7
  =13*56;...........................................................................(i)
  now let wage of 1 boy for 1 day = x;
  wage of 1 man for 1 day =y;
  so a/c quest,
  3*x=2*y................................................(ii)
  now
  (8*7)(40*x+15*y)=15750.........................................(iii)
  from (ii) and (iii)
  x=(15750*2)/(56*125);
  x=4.5;
  y=6.75;
  
  now... no. of dys taken by 20b and 20m to finish the work=z
  z*(1/5*20+1/3*20) = 13*56;
  z=(13*56*15)/20*8;
  z=39*7/4;
  z=9.75 week;
  total amount....
  20(4.5*9.75*7 + 6.75*9.75*7) .............(wage of boy=4.5; wage of men =6.75)
  = 20(307.125 + 460.687)
  = 15356.25.
  so ans total time = 9.75 week and amount =15356.25.
  
• 9 years agoHelpfull: Yes(13) No(1)
• for working:
  3m=5b ==> 1m=(5/3)b
  40b+15m=(8*7)=56 ==> 40b+15m=56
  sub 1m=(5/3)b in 40b+15m=56
  1b=56/65
  sub 1b=56/65 in 40b+15m=56
  1m=3640/3215
  so (20*(56/65))+(20*(3640/3215))=40days
  
  for wages:
  3b=2m ==> 1b=2/3m
  40b+15m=15750
  sub 1b=2/3m in 40b+15m=15750
  1m=378
  1b=252
  20*378+20*252=12600wages
  
  
  
  
  
• 10 years agoHelpfull: Yes(4) No(10)
• I think
  68+(1/4)days & Rs. 19687.5
• 10 years agoHelpfull: Yes(4) No(1)
• 13621 rs..6 weeks approx
• 10 years agoHelpfull: Yes(2) No(2)
• If 65B can do in 56days then how it is possible that 1B will do in 56/65 days?
• 10 years agoHelpfull: Yes(1) No(1)
• Check this out:
  https://testbook.com/bank-clerk-practice/quantitative-aptitude/time-and-work-568a765c9b2dd258e7c25cbf/564b1252d0249b11db16e0d4
• 7 years agoHelpfull: Yes(1) No(0)
• 40boy+15men 1 day work=1/8
  =>8boy+3men 1 day work=1/40
  a/q 3men 1 day work=5 boy 1 day work
  so 8boy+5boy 1 day work=1/40 (using above)
  13boy 1 day work=1/40
  1 boy 1 day work=1/40*13
  so , 1 men 1 day work=1/8*3*13 (1men 1 day work=5*(1 boy 1 day work)/3)
  so 20 men+20 boy 1 day work=4/39 (using above)
  so total weeks taken=39/4=9.75weeks or 68.25 days (ans)
  now,
  a/q 3 boys 1 day wages=2men 1 day wages....(1)
  let 2men 1 day wages=x=>so, 1 men1 day wages=x/2
  so using (1)
  1 boy wages=x/3
  now, a/q
  40*x/3*56+15*x/2*56=15750
  x=(15750*6/56*125)=>13.5
  so 1 men 1 day wages=x/2=>6.75
  and 1 boy 1 day wages=x/3=>4.5
  so, requird wages=(20*6.75*9.75*7)+(20*4.5*9.75*7)=15356.25(ans)
• 7 years agoHelpfull: Yes(1) No(0)
• Anyone, please give us a complete and correct solution .
  Thank You.
• 10 years agoHelpfull: Yes(0) No(0)
• ur solution is ryt @akshay kumar.
• 9 years agoHelpfull: Yes(0) No(0)
• 1 m=5/3 b...;(work relation between men and boys;)
  40 b+15 m does a work in 56 days;
  total work done by 40 b=40*56=2270(boys work a day);
  total work done by 15 men=15*56=840(men day);
  and 1 m= 5/3 b
  therefore 840*5/3=1400 work done by boys in compare to men;
  total work=2270+1400=3670;
  now 20 b+ 20 m==??
  1 m=5/3 b
  20 b+20*5/3=160/3(boys)
  and total work by boys is 3670;
  therefore 3670*3/160=68.7 it is the total days the work will take to complete.
  for wages it is same as Akshay .
  
  
• 8 years agoHelpfull: Yes(0) No(0)
• 6814days,Rs.15356.25
• 7 years agoHelpfull: Yes(0) No(0)
• Let the work of men be M and work of boys be B and their wages be wm and wb
  
  Given 3 men can do as much work as 5 boys and wage of 2 men is equal to wage of 3 boys
  
  ∴ 3M = 5B
  
  ⇒ M = 5B/3
  
  And 2wm = 3wb
  
  ⇒ wm = 3wb/2
  
  40 boys and 15 men work for 8 weeks to complete a job and the work costs 15750
  
  Total work done = 40B + 15M
  
  ⇒ Total work done = 40B + 15 × 5B/3
  
  ⇒ Total work done = 65B
  
  Thus to complete 65B work 8 weeks are required
  
  Total wage = 40wb + 15wm
  
  ⇒ Total wage = 40wb + 45wb/2 = 125wb/2
  
  Given Total cost of work = 15750
  
  Total cost = wage × number of weeks
  
  15750 = 125wb/2 × 8
  
  ⇒ wb = 31.5
  
  If 20 men and 20 boys work then
  
  Total work = 20M + 20B
  
  ⇒ Total work = 20 × 5B/3 + 20B
  
  ⇒ Total work = 160B/3
  
  To complete 65B work it took 8 weeks
  
  ∴ To complete 160B/3 time taken = 8160B3×65B
  
  ⇒ Time taken to complete 160B/3 work = 39/4 = 9 ¾ Weeks
  
  Total wage = 20wm + 20wb
  
  ⇒ Total wage = 30wb + 20wb = 50wb
  
  Total cost = wage × number of weeks
  
  ⇒ Total cost = 50 × 31.5 × 39/4
  
  ⇒ Total cost = 15356.25
• 6 years agoHelpfull: Yes(0) No(0)