Question

The difference between a two digit number and the number obtained by interchanged the two digits of the number is $9$. What is the difference between the two digits of number.

• A. $3$
• B. $2$
• C. $1$
• D. Cannot be determined
• E. None of these

Answer 1

The correct option is C $1$

Let the unit's digit be $y$ and ten's digit be $x$.

Then, the number $=10x+y$. When we interchange the digits, the number will be $10y+x$.

Now, it is given that the difference between a two digit number and the number obtained by interchanged the two digits of the number is $9$, therefore, we have:

$(10x+y)-(10y+x)=9\Rightarrow 9x-9y=9\Rightarrow 9(x-y)=9\Rightarrow x-y=\frac{9}{9}\Rightarrow x-y=1$

Hence, the difference between the two digits of number is $1$.