AMC10 2027 - Self-practice Set 5 Question 5

Question 5

For a positive integer $n$, let $S(n)$ be the sum of its decimal digits; for example, $S(6920)=17$. Suppose $S(n)=1274$. Which of the following could equal $S(n+1)$?

$1$
$3$
$12$
$1239$
$1265$