text: # Discussion of Question with ID = 077 under Time-and-Work
  
  ## This is the discussion forum for this question. If you find any mistakes in the solution, or if you have a better solution, then this is the right place to discuss. A healthy discussion helps all of us, so you are requested to be polite and soft, even if you disagree with the views of others. The question and its current solution has also been given on this page.
  
  ### Question
  
  A, B and C can independently complete a work in 5, 15 and 13 days respectively. B and C start the work together, but A joins them after 2 days. In how many days will the work be completed?
  
  A
  
  \$4{5/67}\$ days.
  
  B
  
  \$5{5/67}\$ days.
  
  C
  
  \$6{5/67}\$ days.
  
  D
  
  \$7{5/67}\$ days.
  
  Soln.
  Ans: a
  
  Use the shortcut formula. If A, B, C can independently complete the job in x, y and z days, and A joins after n days, the work is completed in \${xyz}/{xy + yz + zx}\$ × \$(1 + n/x)\$ days. Putting the various values x = 5, y = 15, z = 13, n = 2, and simplifying, we get \${273/67}\$, which is same as: \$4{5/67}\$.
explanation: The document contains a math question related to time and work, along with a detailed solution and the correct answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Discussion of Question with ID = 077 under Time-and-Work
  
  ## This is the discussion forum for this question. If you find any mistakes in the solution, or if you have a better solution, then this is the right place to discuss. A healthy discussion helps all of us, so you are requested to be polite and soft, even if you disagree with the views of others. The question and its current solution has also been given on this page.
  
  ### Question
  
  A, B and C can independently complete a work in 5, 15 and 13 days respectively. B and C start the work together, but A joins them after 2 days. In how many days will the work be completed?
  
  A
  
  \$4{5/67}\$ days.
  
  B
  
  \$5{5/67}\$ days.
  
  C
  
  \$6{5/67}\$ days.
  
  D
  
  \$7{5/67}\$ days.
  
  Soln.
  Ans: a
  
  Use the shortcut formula. If A, B, C can independently complete the job in x, y and z days, and A joins after n days, the work is completed in \${xyz}/{xy + yz + zx}\$ × \$(1 + n/x)\$ days. Putting the various values x = 5, y = 15, z = 13, n = 2, and simplifying, we get \${273/67}\$, which is same as: \$4{5/67}\$.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question related to time and work, along with a detailed solution and the correct answer.
  
  Label: question-and-answer