If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by

• ALGEBRAIC SUM is 5380. the sum varies(increases) by 330.
  
  Solution:
  Sum of all numbers from 1 to n is given by n(n+1)/2
  so sum of all numbers from 1 to 100 is 100*(100+1)/2 = 5050
  
  6 comes 20times in the numbers from 1 to 100
  6 comes in 'units' place 10 times in the numbers 1 to 100 i.e. 6,16,26,....,96
  6 comes in 'tens' place 10 times in the numbers 1 to 100 i.e. 60,61,62,.....,69
  
  sum of these 6's is 10(6*10)+10(6*1)=600+60=660
  
  if all 6's are replaced by 9
  then sum of those 9's will be 10(9*10)+10(9*1)=990
  
  now algebraic sum will be 5050-660+990= 5380
• 13 years agoHelpfull: Yes(75) No(20)
• from 1 to 100, 6 is used 10 time at unit place and 10 times at tenth place so on replaces it by 9 ,its value increased 30(10*3=30)due to unit place and 300 (10*30 = 300) due to tenth place so total increase will be 330
• 13 years agoHelpfull: Yes(50) No(3)
• 1 11 21 .......91
  2 12 22........92
  3 13 23........93
  . . . .. . .. . .
  . . .. .. . .. .
  . . .. . . .. . ...
  there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column
  and diff of 6 and 9 is 3 so
  3*1*10+3*10*10 = 330
  
• 9 years agoHelpfull: Yes(7) No(3)
• 4720 ...
  
  
  
• 9 years agoHelpfull: Yes(4) No(1)
• if all 6 are replaced with 9 from 1 to 100 then algebric sum would varies by 330.
  explanation
  first take the numbers which have 6 in their unit place - 06,16,26,36,46,56,66,76,86,96.
  if all 6 in unit plce is replaced with 9 then in each case the increment would be 3.
  so for all ten numbers total increment is 10*3=30.
  
  then take all numbers which have 6 in their tenth place - 60,61,62,63,64,65,66,67,68,69
  in each case if we replace 6 with 9 -90,91,92,93,94,95,96,97,98,99
  then there is increment of 30 in each case .
  so total increment for ten numbers is 10*30==300.
  so the total increment including unit and tenth place is 30+300=330
  
• 8 years agoHelpfull: Yes(1) No(0)