Question

The sum of a two digit number and the number obtained by interchanging its digit is 99. Find the number.

Answer 1

Hint: First, let us suppose that tens place digit be x and one place digit be y, then the two digit number can be written as 10x+y. Then, we are told to interchange both digits with their places as y comes to ten places and x goes to one place as 10y+x. Then, we are given the condition in the question that the supposed number which is 10x+y and its reversed digits obtained number which is 10y+x sums to 99 which gives the conditions that define the final result.

Complete step-by-step answer:
In this question, we are supposed to find the two digit number with the condition that the sum of a two digit number and the number obtained by interchanging its digit is 99.
So, before proceeding for this, we must know that to represent a two digit number we need two places values which is tens place and one place.
So, let us suppose that tens place digit be x and ones place digit be y, then the two digit number can be written as:
10x+y
Now, we are said to interchange both digits with their places as y comes to tens place and x goes to ones place.
So, by applying above condition, we get the value as:
10y+x
Now, we are given the condition in the question that the supposed number which is 10x+y and its reversed digits obtained number which is 10y+x sums to 99.
So, by using the above condition, we get the equation as:
$10x+y+10y+x=99$
Then, by solving the above equation, we get:
$\begin{align}
  & 11x+11y=99 \\
 & \Rightarrow 11\left( x+y \right)=99 \\
 & \Rightarrow \left( x+y \right)=\dfrac{99}{11} \\
 & \Rightarrow \left( x+y \right)=9 \\
\end{align}$
So, we get the condition from the above expression as x+y=9.
Then, with the given condition, we get the following set of answers as:
18, 81, 54, 45, 27, 72, 36, 63
So, we get 8 answers for the given condition in the question.
Hence, 18, 81, 54, 45, 27, 72, 36, 63 are the required answers.

Note: Now, to solve these types of questions, we must be careful with the consideration as most of us consider two digit numbers as xy which is wrong as two digits numbers have the representation of tens and ones place which is actually represented by 10x+y.