# I am a three-digit number. My tens digit is five more than the ones digit .my hundred digits is eight less than my tens digit. What number am I?

Answer

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**Hint:**To solve such a question we have to make some conditions and by applying these conditions according to the question we can easily find our number. Range of $3$ digit number is from ($100-999)$ and range of $2$ digit number is ($10-99$).

**Complete step by step solution:**

Let the unit digit to be X then, according to the question x must be greater than equal to zero (as unit place of $100$ is $0$) and it also must be less than or equal to nine (as the highest number in unit place can be equal to $9$). And this is also valid for tens digit so, according to the question the equation forms as X+$5 \le 9$ i.e.,$ X \le4$.

For hundreds digit is eight less than X+$5$ so equation become X+$5-8 \ge 0$ $\Rightarrow X-3 \ge 0 \Rightarrow X \ge 3$ which implies that X greater than $3$ and greater than or equal to $4$. i.e., = $[3,4]$.

And as given in the question

Let the unit digit to be $3$and hence the tens digit become $8$ and the hundreds digit become 0 and number forms as $083$.

Let unit Let unit digit to be $4$ and hence the tens digit become 9 and the hundreds digit become $1$ and number forms as $194$.

And therefore, the number is either $083$ or $194$ and we know that $083$ is a two-digit number and therefore, our required number is $194$.

**Therefore, the three digit number is $194$.**

**Note:**

To solve these types of questions always assume the units digit to be a variable like $X$ and start forming the equation using inequality and solve the equations to find the value of $X$ and then apply conditions given as per question.

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