A can do apiece of work in 14 days which B can do in 21 days, they begin together but 3 days before the completion of the work, A leaves off. the total no of days to complete the work is

(a) 6 3/5 (b) 8 1/2 (c) 10 1/5 (d) 13 1/2

• let total work be 42
  then
  A's 1 day work=3 B's one day work =2
  So,
  5(x-3) + 2*3 = 42
  5x-15+6=42
  5x=51
  x=51/5
  =10 1/5 Ans.
• 9 years agoHelpfull: Yes(2) No(0)
• (x-3)/14 +x/21 =1 then x=51/5 or 10 1/5
• 9 years agoHelpfull: Yes(2) No(0)
• 12 9/10
  
  1 day work of A & B=(1/14)+(1/21)=5/42, so work is proposed to be completed by 42/5 days
  3 days before the completion of the work=(42/5)- 3=27/5 days
  So work completed upto 27/5 days=(5/42)*(27/5)=9/14 and remaining work=5/14
  Days required to complete the remaining work by B=(5/14)/(1/21)=15/2
  So total number of days to complete the work=(27/5) + (15/2)=129/10 or 12 9/10
• 9 years agoHelpfull: Yes(1) No(0)
• Jasmeet, please explain it clearly
• 9 years agoHelpfull: Yes(0) No(0)
• work done by A in 1 day = 1/14
  work done by B in 1 day = 1/21 ----------(equation 1)
  so,work done by A and B in 1 day = 1/14+ 1/21 = 5/42
  so,work done by A and B in 3 days = 5/42 * 3 = 15/42
  
  so, remaining work after 3 days = 27/42
  B alone can do this work in 27/42 / 1/21 = 27/42 * 21/1 = 27/2 days -----(according to equation 1)
  
  
  
  hence ,
  total time = 27/2 + 3 = 33/2 days or 16 1/2 days (answer)
• 9 years agoHelpfull: Yes(0) No(0)
• Vivek The last Thing that u concluded i.e addition of 3 is wrong cause the remaining work is to be calculated by B and the value 13.5 is the total value of days
• 9 years agoHelpfull: Yes(0) No(0)
• First of all take the lcm of(14,21) it will be 42 , that means both A and B contributed 42 unit of work together. Now A can do a piece of work in 14 days that means in 1 day A will contribute 3 unit of work(42/14) and B can do a piece of work in 21 days that means in 1 day B will contribute 2 unit of work.
  
  Now in the question a leaves off 3 days before completion of work, means last 3 days only B will have contributed . If B can contribute 2 unit of work in 1 day then in 3 days B can contribute 6 unit of work.
  
  Now total work unit was 42 and only b (in last 3 days ) contributed 6 unit , remaining both A and B (3 days before completion) will contribute 42-6=36 unit of work.
  
  now in 1 day and B contribute 5 unit of work .
  
  5 (w)---------------------------1(day)
  1(w)-----------------------------1/5(day)
  36(w)---------------------------36/5(days) = 7 1/5
  
  
  not the total days they will complete the work --- 7 1/5+3= 10 1/5
• 6 years agoHelpfull: Yes(0) No(0)