# Ex.16.1 Q4 Playing with Numbers Solutions - NCERT Maths Class 8

Go back to  'Ex.16.1'

## Question

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

\begin{align}{A \;{B}} \\ { +\;3\;{7}} \\ \hline 6\, {A} \\ \hline\end{align}

Video Solution
Playing With Numbers
Ex 16.1 | Question 4

## Text Solution

What is the 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 $$3$$ is giving $$6.$$ There can be two cases.

(1) First step is not producing a carry

In that case, $$A$$ comes to be $$3$$  as $$3 + 3 = 6.$$ Considering the first step in which the addition of $$B$$ and 7 is giving $$A$$ (i.e., $$3$$), $$B$$ should be a number such that the unit’s digit of this addition comes to be $$3.$$ It is possible only when $$B = 6.$$ In this case,$$A = 6 + 7 = 13$$ However, $$A$$ is a single digit number. Hence, it is not possible.

(2) First step is producing a carry

In that case, $$A$$ comes to be $$2$$  as $$1 + 2 + 3 = 6.$$ Considering the first step in which the addition  of  $$B$$ and $$7$$ is giving $$A$$ (i.e., $$2$$), $$B$$ should be a number such that the unit’s digit of this addition comes to be $$2.$$ It is possible only when $$B=5$$ and $$5 + 7 = 12.$$

\begin{align}{2 \;{5}} \\ { +\;3\;{7}} \\ \hline 6\, {2} \\ \hline\end{align}

Hence, the values of $$A$$ and $$B$$ are $$2$$ and $$5$$ respectively.

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school