150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on the third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

• Let x be the number of days in which 150 workers finish the work.
  
  According to the given information,
  
  150x = 150 + 146 + 142 + …. (x + 8) terms
  
  The series 150 + 146 + 142 + …. (x + 8) terms is an A.P. with first term 146, common difference –4 and number of terms as (x + 8)
  
  150x=(x+8)/2[2(150)+(x+8-1)(-4)]
  150x=(x+8)[(150)+(x+8-1)(-4)]
  150x=(x+8)[(150)-2x-14]
  75x=(x+8)(68-x)
  x2+15x-544=0
  (x-17)(x+32)=0
  =>x=17 or x=-32
  However, x cannot be negative.
  
  therefore x = 17
  
  Therefore, originally, the number of days in which the work was completed is 17.
  
  Thus, required number of days = (17 + 8) = 25
  =25 days
• 12 years agoHelpfull: Yes(7) No(3)
• originally, the number of days in which the work was to be completed is 17.
  
  required number of days now = (17 + 8) = 25
• 12 years agoHelpfull: Yes(4) No(4)