# Ex.16.1 Q3 Playing with Numbers Solutions - NCERT Maths Class 8

## Question

Find the value of the letter in the following and give reasons for the steps involved.

\[\begin{align} \begin{array}{c}{1 \;{A}} \\ { \times\,{A}} \\ \hline 9 {A} \\ \hline\end{array} \end{align}\]

## Text Solution

**Reasoning:**

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

**What is known?**

Multiplication operation of two numbers.

**What is unknown?**

Value of alphabet i.e \(A\)

**Steps:**

The multiplication of \(A\) and \(A\) gives a number whose one's digit is \(A\) again. Hence , \(A\) must be \(1\) or \(6.\)

Let \(A\) be \(1,\)

Therefore, \(A \times A = 1 \times 1 = 1 \ne 9\)

So, this is not possible for any value of \(A.\)

Hence\(,A\) must be \(6 \) only.

For \(A=6,\text{ we get }A \times A = 6 \times 6 = 36\)

and \(3\) will be a carry for the next step.

\(\therefore\) \(A\times1=6\times1+3\) (Carried on ) \(= 9 \)

\[\begin{align}\begin{array}{c}{1 \;{6}} \\ { \times\,{6}} \\ \hline 9 {6} \\ \hline\end{array}\end{align}\]

Hence, the value of \(A\) is \(6.\)