# Ex.16.1 Q4 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.

\[\begin{align}{A \;{B}} \\ { +\;3\;{7}} \\ \hline 6\, {A} \\ \hline\end{align}\]

## Text Solution

**What is the 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 \(3\) is giving \(6.\) There can be two cases.

**(1) First step is not producing a carry **

In that case, \(A\) comes to be \(3\) as \(3 + 3 = 6.\) Considering the first step in which the addition of \(B\) and 7 is giving \(A\) (i.e., \(3\)), \(B\) should be a number such that the unit’s digit of this addition comes to be \(3.\) It is possible only when \(B = 6.\) In this case,\(A = 6 + 7 = 13\) However, \(A\) is a single digit number. Hence, it is not possible.

**(2) First step is producing a carry **

In that case, \(A\) comes to be \(2\) as \(1 + 2 + 3 = 6.\) Considering the first step in which the addition of \(B\) and \(7\) is giving \(A\) (i.e., \(2\)), \(B\) should be a number such that the unit’s digit of this addition comes to be \(2.\) It is possible only when \(B=5\) and \(5 + 7 = 12.\)

\[\begin{align}{2 \;{5}} \\ { +\;3\;{7}} \\ \hline 6\, {2} \\ \hline\end{align}\]

Hence, the values of \(A\) and \(B\) are \(2\) and \(5\) respectively.