Question

Find sum of all 3 digit number which leaves reminder 3 when divided by 5.

Answer 1

• smallest 3 digit number which leave the remainder 3 when divided by 5 =103
  largest 3 digit number which leave the remainder 3 when divided by 5 =998
  3 digit number after 103 which leave the remainder 3 when divided by 5 =108
  an ap is formed: 103,108........998
  first term=103
  common difference=5
  let the total no. of three digit numbers which leave the remainder 3 when divided by 5=n
  998=103+(n-1)5
  180=n
  sum of ap=180/2 *(103+998)=90*1101
  =99090