a is 50% as efficient as b . c does half of the work done by a and b togetherif c alone does the work in 20 days,then a,b and c together can do the work in how many days?

• 6 2/3 days
  
  Let a,b and c can complete the work in A, B and C days respectively, then
  I) a is 50% as efficient as b, so a requires twice the days required by b => A=2B ---(i)
  II) c does half of the work done by a and b together => 1/C = (1/2)(1/A + 1/B) ---(ii)
  III) 1/C=1/20 ---(iii)
  Comparing (ii) & (iii), 1/20=(1/2)(1/A + 1/B) => 1/A + 1/B =1/10 ---(iv)
  Substituting A=2B from (i) in (iv), we get 1/2B + 1/B= 1/10 => 1/B=1/15, so 1/A= 1/30
  1 days work of a, b, & c = 1/A + 1/B + 1/C = 1/30 + 1/15 + 1/20 = 9/60= 3/20
  Hence required days = 20/3 = 6 2/3
• 7 years agoHelpfull: Yes(16) No(2)
• try to use percentage concept to solve this kind of problem.
  Now, See the solution:
  C completes a work in 20 days who is half efficient of A and B together i.e, A and B finishes that work together in 10 days.
  Now C work of a day=5%
  A and B works of a day=10%
  So A, B and C works of a day=5+10=15%
  To acquire 100%(for work completion), Days=100/15=6*2/3 days.
• 7 years agoHelpfull: Yes(3) No(1)
• given,
  a is 150% efficicient than b
  therefore Efficiency ratio of a:b=150:100 =>3:2
  Ratio of time taken by a and b is=2:3
  let a ,b,c takes x,y,z days respectievely to complete the work
  1 day work of a &b=1/x + 1/y
  therefore, 1 day work of c=(1/x +1/y)/2=1/z
  =>1/20=(1/x+1/y)/2 ( c's 1 day work =1/20)
  =>1/x + 1/y =1/10
  now, 1 day work of a,b and c =1/10 +1/20 =3/20
  therefore a ,b and c can complete the work in 20/3 days.
• 7 years agoHelpfull: Yes(2) No(1)
• Let
  A's one day work = 3
  Then, B's one day work will be = 2 days (Since B is 50% more efficient than A )
  C does half the work done by A and B, So
  C's one day work = (3+2)/2
  Therefore,
  Work Ratio of 1 day for A, B and C is = 3 : 2 : 5/2
  On Simplification Ratio becomes = 6 : 4 : 5
  Therefore,
  C completes the work in 20 days so
  Total work = 5*20 = 100
  A, B and C can together do the work in = 100 / (6 + 4+ 5)= 20/3 days
  
  Ans. 20/3 days
• 7 years agoHelpfull: Yes(2) No(0)
• Ans is correct = 6 2/3 , but Mr. Devendra said that , a and b are in ratio 2:1 , NO
  a is 150% of b so ther are in ratio 3:2 .
• 7 years agoHelpfull: Yes(0) No(3)
• ans is 20/3
• 7 years agoHelpfull: Yes(0) No(1)
• let b=> x part
  a=> 2x part
  if we take the L.C.M. ,total they done 2x part
  b-> x | 1day-2part
  a->2x| 1day-1part
  total in 1day they do(2+1=3part)
  3part->1day
  1part->1/3day
  2xpart->2x/3days
  
  according to question c does half of work and complete that task in 20 days
  so time taken by c is, 2*2x/3=4x/3;
  4x/3=20
  x=15(time taken by b to complete task)
  2x=30(time taken by a to complete task)
  
  a=30|1day-4part
  b=15|1day-8part
  c=20|1day-6part
  lcm=120
  (4+8+6=18part)
  18part-1day
  120part-120/18=20/3
• 7 years agoHelpfull: Yes(0) No(0)
• Let the whole work is =100%
  c does 100% work in 20 days.
  C's 1 day work=100/20=>5
  According to question C is doing half the work done by A & B together; doesn’t it means that A + B together do 2*c one day work=5*2=>10
  (A+B+C) one day work is 15
  100% work done by (A+B+C)=100/15=>6.666
• 7 years agoHelpfull: Yes(0) No(0)
• 6 days 18 hr
• 6 years agoHelpfull: Yes(0) No(0)