Question

Find the values of the letters in the following and give reasons for the steps involved.

Answer 1

Hint: First we will find the value of B by taking the last column of the given sum \[1 + {\text{B}} = 0\].
Then we will have a carry-over of 1 on the first column of the given sum, which is the tens value of the sum of the last column of the given sum. Then we will have to add 1 with the middle column of the given sum to find the value of A.

Complete step-by-step answer:
We are given that

We know that the sum is the result of adding two or more numbers.
First, we will take the last column of the given sum \[1 + {\text{B}} = 0\].
Then we know that B has to be 9 because the unit digit of the sum has to be 0 as only when 1 is added to 9, we get 10.
This implies that \[{\text{B}} = 9\].
Now we have sum as

So, we will have a carry-over of 1 on the middle column of the given sum, which is the tens value of the sum of the last column of the given sum.

Thus we will have to add 1 with the middle column of the given sum, we get
\[ \Rightarrow {\text{A}} + 1 + 1 = 9\]
Rewriting the above equation, we get
\[ \Rightarrow {\text{A}} + 2 = 9\]

Subtracting the above equation by 2 on both sides, we get
\[
   \Rightarrow {\text{A}} + 2 - 2 = 9 - 2 \\
   \Rightarrow {\text{A}} = 7 \\
 \]
Hence, we have A is 7.
Therefore, the value of A is 7 and B is 9.

Note: In solving these types of questions, you need to know that a sum is a result of adding two or more numbers, by bringing two or more numbers together to make a new total. One needs to know that the number, which is a carry-over will be added to the first column of the given sum or else the solution will be wrong. We can also find the sum by counting our fingers for better understanding.