There are a certain number of pages in a book. arjun tore a certain page out of the book and later found that tha average of the remaining page numbers is 46*10/13(fraction). which of the following were the page number of the page that arjun had torn?
a) 57 and 58
b)59 and 60
c)45 and 46

• For understanding this, draw a timeline.
  
  It is the sum of consecutive numbers starting from 1 to an even number. So,
  sum of all page numbers = n(n+1)/2 and the average = n(n+1)/2/n = (n+1)/2
  
  Calculating the range by which the average can vary when any page is torn:
  Case I : Least value page numbers are torn = (1 and 2)
  Assuming total page numbers to be 8.
  new average = ((8(8+1)/2)-(1+2))/(8-2) = 5.5
  
  Case II : Greatest value page numbers are torn = (7 and 8)
  new average = ((8(8+1)/2)-(7+8))/(8-2) = 3.5
  
  Actual average when no page is torn = (8(8+1)/2)/8 = 4.5
  
  
  It means if any page is torn then the average of the page numbers will lie between (Actual average +- 1)
  
  So, here 460/13 = 35.38 which means that the actual average must have been 34.5 or 35.5
  
  But rejecting 34.5 as all options are of greater value that means average will shift towards the lesser value. 35.38 is lesser to 35.5.
  
  So, if 35.5 is the average of all page numbers then total page numbers = 70
  
  Now, ((70*(70+1)/2)- (sum of option c))/(70-2) = around 35.38 (ie. 46*10/13)
• 6 years agoHelpfull: Yes(2) No(10)
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• 7 years agoHelpfull: Yes(0) No(2)