# Ex.16.1 Q8 Playing with Numbers Solutions - NCERT Maths Class 8

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## Question

Find the values of the letters in the following and give reasons for the steps involved.

\begin{align}{A \;\;{1}} \\ { +\;1\;\, {B}} \\ \hline B\;\; {0} \\ \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 $$1$$ and is giving $$0$$ i.e., a number whose one’s digits is $$0.$$ This is possible only when digit $$B$$ is $$9.$$ In that case, the addition of $$1$$ and $$B$$ will give $$10$$ and thus, $$1$$ will be the carry for the next step. In the next step,

$1 + A + 1 = B$

Clearly, $$A$$ is $$7$$  as $$1 + 7 + 1 = 9 =B$$

Therefore, the addition is as follows.

\begin{align}{7 \;\;{1}} \\ { +\;1\;\, {9}} \\ \hline 9\;\; {0} \\ \hline\end{align}

Hence, the values of and are $$7$$ and $$9$$ respectively.

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