A 3–digit number 4a3 is added to another 3–digit
number 984 to give the four-digit number 13b7,
which is divisible by 11. Then, (a + b) is

Question

Accepted Answer

To solve the problem, we need to determine the values of $$a$$ and $$b$$ such that:

1. The equation $$4a3 + 984 = 13b7$$ holds true.
2. The number $$13b7$$ is divisible by 11.

### Steps:

**1. Divisibility Rule for 11:**  
   A number is divisible by 11 if the difference between the sum of its digits at odd positions and the sum of its digits at even positions is divisible by 11 or equals zero.  
   For $$13b7$$:  
   $$
   (7 + 3) - (b + 1) = 9 - b
   $$  
   Setting $$9 - b = 0$$, we find $$b = 9$$.

**2. Find $$a$$:**  
   Substitute $$b = 9$$ into the equation:  
   $$
   4a3 + 984 = 1397
   $$  
   Solve for $$a$$:  
   $$
   a + 8 = 9 \implies a = 1
   $$

**3. Sum of $$a + b$$:**  
   With $$a = 1$$ and $$b = 9$$, their sum is:  
   $$
   a + b = 1 + 9 = 10
   $$

### Final Answer:  
The value of $$a + b$$ is **10**.

Answer

Answer

Answer