# Ex.16.1 Q9 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.

\[\begin{align}&2\;\;A \;\;{B} \\ +&A\;\,B\;\; {1} \\ \hline &B\;\;1\;\; {8} \\ \hline\end{align}\]

## 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 \(B\) and \(1\) is giving \(8\) i.e., a number whose one’s digits is \(8.\) This is possible only when digit \(B\) is \(7.\) In that case, the addition of \(B\) and \(1\) will give \(8.\) In the next step,

\[A + B = 1\]

Clearly, \(A\) is \(4.\)

\(4 + 7 = 11\) and \(1\) will be a carry for the next step. In the next step,

\[1 + 2 + A = B\]

\[1 + 2 + 4 = 7\]

Therefore, the addition is as follows.

\[\begin{align}&2\;\;4 \;\;{7} \\ +&4\;\,7\;\; {1} \\ \hline &7\;\;1\;\; {8} \\ \hline\end{align}\]

Hence, the values of \(A\) and \(B\) are \(4\) and \(7\) respectively.