Question

The difference between a two digit number and the number obtained by the interchanging the digits is 27. What is the difference between the two digits of the number?

Answer 1

Step 1. Determine the numbers.

The expression of a two digits number is $10x+y$.

The number obtained by reversing the digit is $10y+x$.

So, the numbers are $10x+y$ and $10y+x$.

Step 2. Subtract the numbers.

Find the difference of the two numbers:

$\begin{array}{rcl}10x+y-\left(10y+x\right)& =& 10x+y-10y-x\\ & \Rightarrow & 10x+y-\left(10y+x\right)=9x-9y\\ & \Rightarrow & 10x+y-\left(10y+x\right)=9\left(x-y\right)\end{array}$

The difference between the numbers is $27$:

So, $\begin{array}{rcl}9\left(x-y\right)& =& 27\\ & \Rightarrow & x-y=3\end{array}$

So, the difference between the digits of the numbers is $3$.