# Ex.16.1 Q10 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}&1\;\;2 \;\;{A} \\ +\;&6\;\,A\;\; {B} \\ \hline &A\;\;0\;\; {9} \\ \hline\end{align}

Video Solution
Playing With Numbers
Ex 16.1 | Question 10

## 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 $$A$$ and $$B$$ is giving $$9$$ i.e., a number whose ones digits is $$9.$$ The sum can be $$9$$ only as the sum of two single digit numbers cannot be $$19.$$ Therefore, there will not be any carry in this step.

In the next step, $$2 + A = 0$$

It is possible only when $$A = 8$$

$$2 + 8 = 10$$ and $$1$$ will be the carry for the next step.

$$1 + 1 + 6 = A$$

Clearly, $$A$$ is $$8.$$ We know that the addition of $$A$$ and $$B$$ is giving $$9.$$ As $$A$$ is $$8,$$ therefore, $$B$$  is $$1.$$

Therefore, the addition is as follows.

\begin{align}&1\;\;2 \;\;{8} \\ +\;&6\;\,8\;\; {1} \\ \hline &8\;\;0\;\; {9} \\ \hline\end{align}

Hence, the values of $$A$$ and $$B$$ are $$8$$ and $$1$$ respectively.

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