Consider all the natural numbers. they can end with any one of these 1,2,3,4,5,6,7,8,9 or 0.
if a number ending with 1 is divided by 10, the remainder is 1,
if a number ending with 2 is divided by 10, the remainder is 2,
similarly see all the numbers ending with 3,4,5,6,7,8 and 9......u will see that the remainders are 3,4,5,6,7,8 and 9 respectively.
if the number ends with 0 there is no remainder when divided by 10.
Thus when any natural number is divided by 10, the sum of all possible remainders is 1+2+3+4+5+6+7+8+9 = 45