Two two-digit numbers, 'AB' and 'BA', sum to produce a three-digit number in which the second d

igit

is equal to A. The addition is represented below. (Note
that the variables are used to represent individual digits;

no mu

ltiplication is

taking place).
AB + B

A= 1A2
What

is B?

9

Explanation:

Another way to represent this question is:

+ AB BA1A2

In the one's column, B and A add to produce a number with a two in the one's place. In the ten's column, we can see that a one must carry in order to get a digit in the hundred's place. Together, we can combine these deductions to see that the sum of A and B must be twelve (a one in the ten's place and a two in the one's place).

In the one's column: B+A=12

The one carries to the ten's column.

In the ten's column: (1)+A+B=(1)+12=13

The three goes into the answer and the one carries to the hundred's place. The final answer is 132. From this, we can see that A=3 because 1A2=132.

Using this information, we can solve for B.

A+B=12 and A=3

3+B=12

B=9