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

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

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

 Video Solution
Playing With Numbers
Ex 16.1 | Question 3

Text Solution


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 \(A\)


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 \(6.\)