Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

Given :

Sum of the digits of a two-digit number$=9$.

When we interchange the digits, it is found that the resulting new number is greater than the original number by 27.

To do :

We have to find the two-digit number.

Solution :

Let the unit digit be y and tens digit be x.

The number formed $= 10x + y$

The reverse number $= 10y + x$

Therefore,

$x + y = 9$.........................(i)

$10y + x = (10x + y) + 27$

$ 10y - y + x -10x = 27$

$9y - 9x =27$

$y-x =3$

$y=x+3$.................(ii)

Substitute (ii) in (i)

$x + (x+3) = 9$

$2x + 3 = 9$

$2x = 6$

$x = \frac{6}{2} = 3$

$y= 3+3 = 6$

So, $x = 3, y= 6$

Therefore, the original number is 36.

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Updated on: 10-Oct-2022

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