# Ex.16.1 Q10 Playing with Numbers Solutions - NCERT Maths Class 8

## Question

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

\[\begin{align}&1\;\;2 \;\;{A} \\ +\;&6\;\,A\;\; {B} \\ \hline &A\;\;0\;\; {9} \\ \hline\end{align}\]

## Text Solution

**What is known?**

Addition operation of two numbers

**What is unknown?**

Value of alphabets i.e. \(A\) and \(B.\)

**Reasoning:**

Each letter in the puzzle must stand for just one digit. Each digit must be represented by just one letter.

**Steps:**

The addition of \(A\) and \(B\) is giving \(9\) i.e., a number whose ones digits is \(9.\) The sum can be \(9\) only as the sum of two single digit numbers cannot be \(19.\) Therefore, there will not be any carry in this step.

In the next step, \(2 + A = 0\)

It is possible only when \(A = 8\)

\(2 + 8 = 10\) and \(1\) will be the carry for the next step.

\(1 + 1 + 6 = A\)

Clearly, \(A\) is \(8.\) We know that the addition of \(A\) and \(B\) is giving \(9.\) As \(A\) is \(8,\) therefore, \(B\) is \(1.\)

Therefore, the addition is as follows.

\[\begin{align}&1\;\;2 \;\;{8} \\ +\;&6\;\,8\;\; {1} \\ \hline &8\;\;0\;\; {9} \\ \hline\end{align}\]

Hence, the values of \(A\) and \(B\) are \(8\) and \(1\) respectively.