Q. A group of men can complete a job in X hours. After every 4 hours, half the number of men working at that point of time leave the job. Continuing this way if the job is finished in 16 hours, what is the value of X.

• If there are m men
  
  job requires mX man hours.
  
  job completed in first 4 hrs = m*4 =4m
  job completed in next 4 hrs = 4*m/2 = 2m
  job completed in next 4 hrs = 4.m/4 = m
  job completed in last 4 hrs = 4.m/8= m/2
  4m+2m+m+m/2 = mX
  x= 7+1/2 = 7.5 days
  
• 12 years agoHelpfull: Yes(10) No(2)
• x= 7.5 hours.
  
  If all the men continued their work together for all days, they will complete work in 7.5 hours. ( There was a mistake in previous post)
  As per condition, men are reducing in between , so they took 16 hours.
• 12 years agoHelpfull: Yes(4) No(0)
• If there are m men
  
  job requires mX man hours.
  
  job completed in first 4 hrs = m*4 =4m
  job completed in next 4 hrs = 4*m/2 = 2m
  job completed in next 4 hrs = 4.m/4 = m
  job completed in last 4 hrs = 4.m/8= m/2
  4m+2m+m+m/2 = mX
  x= 7+1/2 = 7.5 hours
• 12 years agoHelpfull: Yes(4) No(1)
• In the Question itself, they gave,
  
  Job finished in 16hours.
  
  So, a group of men can complete a job in X hours means,
  
  X = 16 hours
• 12 years agoHelpfull: Yes(2) No(4)
• x= 7.5 hours.
  
  If all the men continued their work together for all days, they will complete work in 7.5 days.
  As per condition, men are reducing in between , so they took 16 hours.
• 12 years agoHelpfull: Yes(2) No(0)
• Ans. The value of X = 8 hours.
  
  Explanation :
  
  The group will do part of job in 4 days = 4/x , then half of them left the job.
  
  The these remaining half number of men will do the part of job in next 4 days = 2/x, then half of them left the job.
  
  Then these remaining half number of men will do the part of job in next 4 days = 1/x, then half of them left the job.
  
  Then these remaining half number of men will do the part of job in next 4 days = 1/2x, then half of them left the job.
  
  this process continued and the job finished in 16 days.
  
  So 4/x+2/x+1/x+1/2x+........ = 1
  => 1/x(4+2+1+1/2+1/4+..........) = 1
  LHS is an infinite G P series with first term 4/x and common ratio 1/2
  So sum of this series
  
  (1/x)*(4/(1-1/2)) = 1
  => 8/x = 1 => x = 8
  Hence the value of x is 8.
  
  
  
  
• 12 years agoHelpfull: Yes(0) No(2)