# Ex.16.1 Q7 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}} \\ { \times \;\;\,{6}} \\ \hline B\,B\, {B} \\ \hline\end{align}

Video Solution
Playing With Numbers
Ex 16.1 | Question 7

## Text Solution

What is known?

Multiplication 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 multiplication of $$6$$ and $$B$$ gives a number whose one’s digit is $$B$$ again.

It is possible only when

$$B = 0, \;2,\; 4,\; 6,$$ or $$8$$

If $$B = 0,$$ then the product will be $$0.$$ Therefore, this value of $$B$$ is not possible.

If $$B = 2$$, then $$B \times 6 = 12$$ and $$1$$ will be a carry for the next step.

$$6{\text{A}} + 1 = {\text{BB}} = 22 \Rightarrow 6{\text{A}} = 21$$ and hence, any integer value of $$A$$ is not possible.

If $$B = 6,$$ then $$B \times 6 = 36$$ and $$3$$ will be a carry for the next step.

$$6A + 3 = BB = 66 \Rightarrow 6A = 63$$ and hence, any integer value of $$A$$ is not possible.

If $$B = 8,$$ then $$B \times 6 = 48$$ and $$4$$ will be a carry for the next step.

$$6{{A}} + 4 = {{BB}} = 88 \Rightarrow 6{{A}} = 84$$ and hence, $$A = 14.$$ However, $$A$$ is a single digit number.

Therefore, this value of $$A$$ is not possible.

If $$B = 4,$$ then $$B \times 6 = 24$$ and $$2$$ will be a carry for the next step.

$$6A + 2 = BB = 44 \Rightarrow 6A = 42$$ and hence, $$A = 7$$

The multiplication is as follows.

\begin{align}{7 \;\;{4}} \\ { \times \;\;\,{6}} \\ \hline 4\,4\, {4} \\ \hline\end{align}

Hence, the values of $$A$$ and $$B$$ are $$7$$ and $$4$$ respectively.

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