Question

Find the values of the letters in the following and give reasons for the steps involved.
\[
  {\text{ }}1{\text{ 2 A}} \\
  \underline { + {\text{ 6 A B}}} \\
  \underline {{\text{ A 0 9}}} \\
 \]

Answer 1

Hint: We will first consider the given expression. As we have to find the values of the letters we will start with the extreme right side that is with the values of \[{\text{A}}\] and \[{\text{B}}\]. Sum of \[{\text{A}}\] and \[{\text{B}}\] is given as 9 so, we can use the hit and trial method and assume the values of \[{\text{A}}\] and \[{\text{B}}\]. Let us say we take \[{\text{A = 8}}\] and \[{\text{B = 1}}\] which gives the sum as 9. Next, we will consider this process to satisfy all values.

Complete step-by-step answer:
We will first consider the given expression that is
\[
  {\text{ }}1{\text{ 2 A}} \\
  \underline { + {\text{ 6 A B}}} \\
  \underline {{\text{ A 0 9}}} \\
 \]
Now, we have to find the values of the letters in the expression.
We will start with the extreme right column that is the sum of \[{\text{A}}\] and \[{\text{B}}\] is given as 9.
Here we will use a hit and trial method to find the values of \[{\text{A}}\] and \[{\text{B}}\].
So, we have chosen the values of \[{\text{A}}\] as 8 and \[{\text{B}}\] as 1 which gives the sum as 9.
Now, moving to the middle column where the sum of 2 and \[{\text{A}}\] is given as 0.
Here, we will put the value of \[{\text{A}}\] that is 8 and adding 2 gives us the result as 10.
Thus, we will put the units digit that is 0 in the answer row and the tens digit that is 1 as carry over.
Now, moving to the third column, where the sum of 1 and 6 with the carry over 1 gives the result as 8 that is the value, we have chosen in the first column.
Thus, we can conclude that the value of \[{\text{A}}\] as 8 and \[{\text{B}}\] as 1.

Note: While using the hit and trial method, remember to choose the values such as the values satisfy the other sums also. In the middle row the sum is 10 so put the units place digit and use the tens place digit as carry over. Don’t forget to add the carry over in the sum in the last column. If all the values of \[{\text{A}}\] are coming the same then the value chosen is correct.