SPOJ Adding reversed number in Java
First, note that this review is of general good coding practices for production code, and not all suggestions will be appropriate for the sphere of "competitive programming", in which I have no significant experience.

Some thoughts:

For readability, use whitespace consistently and more frequently. There should be whitespace (0) after control statements (if, while, for), around operators (+, %, ..), and before curly braces ({).

In Java, the convention is that open curly braces go on the same line, not on a newline.

Use final aggressively when variable declarations will not change to reduce cognitive load on readers.

AutoCloseable resources such as Scanner should be used in a try-with-resources block to ensure they get closed.

a and b are poor choices for variable names because they're meaningless. Variable names should describe the value they hold. You probably don't even need the intermediate variables.

Methods not intended for use outside their class should be private. Always prefer the most restrictive access you can reasonably apply.

In a real application, it would be highly preferable to having the reversed sum pushed back to the main() method to handle printing. This gives you flexibility, rather than pushing your output choice through your code - if you want to change later, it changes in fewer, higher-level places. 

It might be nice to use the number of cases they provide you with. 

Don't throw Exception ever - throw the most specific checked exception possible. Don't declare thrown checked exceptions if you don't actually throw them.

Your algorithm is much more complex than it needs to be. Lists are extraneous. The problem can be solved with math.

If you were to apply all the changes I suggested, your code might look more like:

import java.util.Scanner;

class Main {

    public static void main(final String[] args) {
        try (final Scanner sc = new Scanner(System.in)) {
            final int numberOfCases = sc.nextInt();
            for (int i = 0; i &lt; numberOfCases; i++) {
                final int firstNumber = sc.nextInt();
                final int secondNumber = sc.nextInt();
                System.out.println(addReversedNumbers(firstNumber, secondNumber));
            }
        }
    }

    private static int addReversedNumbers(final int firstNumber, final int secondNumber) {
        return reverseNumber(reverseNumber(firstNumber) + reverseNumber(secondNumber));
    }

    private static int reverseNumber(final int number) {
        int numberToReverse = number;
        int reversedNumber = 0;

        while (numberToReverse &gt; 0) {
            final int digit = numberToReverse % 10;
            numberToReverse /= 10;
            reversedNumber = 10 * reversedNumber + digit;
        }
        return reversedNumber;

    }

}