# Ex.16.1 Q9 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}&2\;\;A \;\;{B} \\ +&A\;\,B\;\; {1} \\ \hline &B\;\;1\;\; {8} \\ \hline\end{align}

Video Solution
Playing With Numbers
Ex 16.1 | Question 9

## Text Solution

What is known?

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 $$B$$ and $$1$$ is giving $$8$$ i.e., a number whose one’s digits is $$8.$$ This is possible only when digit $$B$$ is $$7.$$ In that case, the addition of $$B$$ and $$1$$ will give $$8.$$ In the next step,

$A + B = 1$

Clearly, $$A$$ is $$4.$$

$$4 + 7 = 11$$ and $$1$$ will be a carry for the next step. In the next step,

$1 + 2 + A = B$

$1 + 2 + 4 = 7$

Therefore, the addition is as follows.

\begin{align}&2\;\;4 \;\;{7} \\ +&4\;\,7\;\; {1} \\ \hline &7\;\;1\;\; {8} \\ \hline\end{align}

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

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