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If $$21y5$$ is a multiple of $$9$$, where $$y$$ is a digit, what is the value of $$y$$?
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## QuestionMathsClass 8

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

$$9$$
4.6
4.6

## Solution

Given:$$21y5$$ is a multiple of $$9$$.
Therefore according to the divisibility rule of $$9$$, the sum of all the digits should be a multiple of $$9$$.
That is, $$2 + 1 + y + 5 = 8 + y$$
Therefore, $$8 + y$$ is a factor 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.
Therefore, the value of $$y$$ should be $$1$$ only i.e. $$8 + y = 8 + 1 = 9$$.