A 3-digit number 4A3 is added to another 3-digit number 984 to give four digit number 13B7, which is divisible by 11. Find (A + B).

Given, a 3-digit number 4A3

And a 3-digit number 984

Both the numbers are added to get a four-digit number 13B7

And 13B7 is divisible by 11.

By observation we get A + 8 = B

⇒ B-A = 8

Since, 13B7 is divisible by 11 to know its divisibility we have to subtract sum of odd placed numbers and sum of even placed numbers

We get,

(7 + 3)-(B + 1) = 9-B = 0

⇒B = 9

Solving, B in B-A = 8 we get

⇒ 9-A = 8

⇒ A = 9-8

⇒ A = 1

Hence, A = 1, B = 9 and (A + B) = 10