To find the value of (X+Y), we need to first understand the given information.

We are given a 3-digit number 4X3, where X represents a missing digit.

When this number is added to 984, we get a 4-digit number 13Y7.

Since the 4-digit number 13Y7 is divisible by 11, we can use the divisibility rule for 11 to find the value of Y.

According to the divisibility rule, the difference between the sum of the digits in the odd positions (1st and 3rd) and the sum of the digits in even positions (2nd and 4th) must be divisible by 11.

So, in the 4-digit number 13Y7, the difference between (1 + 7) and (3 + Y) must be divisible by 11.

This gives us (8 - Y) being divisible by 11.

To get a 4-digit number, the minimum possible value for Y can be 0. In this case, (8 - 0) is divisible by 11, and the number is 1370.

Now, let`s analyze the options given:

Option 1: