# Ex.16.2 Q1 Playing with Numbers Solutions - NCERT Maths Class 8

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## Question

If $$21y5$$ is a multiple of $$9,$$ where $$y$$ is a digit, what is the value of $$y$$?

Video Solution
Playing With Numbers
Ex 16.2 | Question 1

## Text Solution

What is known?

A puzzled number

What is unknown?

Value of the alphabet i.e. $$y.$$

Reasoning:

If the sum of all digits of a number is equal to $$9,$$ then the number is a multiple of $$9.$$

Steps:

If a number is a multiple of $$9,$$ then the sum of its digits will be divisible by $$9.$$

Sum of digits of

$21y5 = 2 + 1 + y + 5 = 8 + y$

Hence, $$8 + y$$ should be a multiple of $$9.$$

This is possible when $$8 + y$$ is any one of these numbers $$0,\; 9, \;18, \;27,$$ and so on ...

However, since $$y$$ is a single digit number, this sum can be $$9$$ only.

\begin{align} 8 + y &= 9\\ y &= 9 - 8\\ y &= 1 \end{align}

Therefore, $$y$$ should be $$1$$ only.

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