Question

The sum of the digits of a two-digit number is 5. The number obtained by reversing the order of digits diminished the original number by 9. Find the number.

Answer 1

Hint – Here we will proceed by using the approach of linear equations in two variables and by substituting the values of one equation into another.

Complete step-by-step answer:
Let the digit at units place = $x$
Let the digit at tens place = $y$
It is given that the sum of digits in the number that is,
$x + y = 5$ …. (1)
Also, it is given that the number obtained by reversing the order of digit diminishes the original number by 9 which is,
$10x + y = 10y + x - 9$ ….. (2)
Now, equation (1) can also be written as
$y = 5 - x$ …. (3)
By taking equation (2), we get,
$10x - x + y - 10y = - 9$ (By transposing)
$9x - 9y = - 9$
$9y - 9x = 9$ (By transferring the subtraction’s operator)
Take 9 as common,
$
  9\left( {y - x} \right) = 9 \\
  y - x = \dfrac{9}{9} \\
 $
$y - x = 1$ (By dividing) … (4)
Now by using substitution method,
Put equation (3) in equation (4)
$\left( {5 - x} \right) - x = 1$ … (As $y = 5 - x$ )
$5 - 2x = 1$
$ - 2x = 1 - 5$
$
   - 2x = - 4 \\
  x = \dfrac{{ - 4}}{{ - 2}} \\
 $
$x = 2$ …. (5)
Now putting value of equation (5) in equation (3),
$
  y = 5 - 2 \\
  y = 3 \\
 $
We can say that the value of the original number is 10y+x that is
10$ \times \left( 3 \right)$+2
=30+2
=32
Hence, the number is 32.

Note – Whenever we come up with this type of problem, then one must know that there are so many methods to solve such types of questions. That is elimination method, cross- multiplication method. (Here we used a substitution method). It should be noted that we can put the value of x in any equation.