# Ex.16.2 Q2 Playing with Numbers Solutions - NCERT Maths Class 8

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## Question

If $$31z5$$ is a multiple of $$9,$$ where $$z$$ is a digit, what is the value of $$z$$?

You will find that there are two answers for the last problem. Why is this so?

## 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

$31z\,5 = 3 + 1 + z + 5 = 9 + z$

Hence, $$9 + z$$ should be a multiple of $$9.$$

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

However, since $$z$$  is a single digit number, this sum can be either $$9$$ or $$18.$$

$$9+z =9\\z=9-9\\z=0$$

Therefore, $$z$$ should be either $$0$$ or $$9.$$

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