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 A by taking the second column of the given sum \[{\text{A}} + 5 = 2\] for the unit digit of the sum has to be 3. Then there will be a carry-over of 1 on the first column of the given sum and add 1 with the first column of the given sum to compute the value of B.

Complete step by step solution: We are given that

We know that the sum is the result of adding two or more numbers.

First, we will take the second column of the given sum \[{\text{A}} + 5 = 2\].
Then we know that A has to be 7 because the unit digit of the sum has to be 2 as only when 7 is added to 5, we get 12.
This implies that \[{\text{A}} = 7\].

So, 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 second column of the given sum.

Thus we will have to add 1 with the first column of the given sum, we get
\[
   \Rightarrow 3 + 2 + 1 = {\text{B}} \\
   \Rightarrow 6 = {\text{B}} \\
   \Rightarrow {\text{B}} = 6 \\
 \]

Therefore, the value of A is 7 and B is 6.

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.