# The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.

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Hint: For example, 27 is a digit number then the sum of digits of number is 2+7=9. Interchanging digits of the number gives a new number that is 27 becomes 72.

Let the required number is xy, that means ten’s place of the digit of required number be x and the units place of the digit be y. Then,

$x + y = 12$ ..... (1)

Required Number =$\left( {10x + y} \right)$.

After interchanging the digits number will be$(10y + x)$.

Given that the number formed by interchanging the digits of the original number exceeds the original number by 18.

$ \Rightarrow \left( {10y + x} \right) - (10x + y) = 18$

$ \Rightarrow 9y - 9x = 18$

$ \Rightarrow y - x = 2$ ..... (2)

On adding equations (1) and (2), we get

$\eqalign{

& 2y = 14 \cr

& \Rightarrow y = 7 \cr} $

Therefore, $x = 12 - 7 = 5$

Hence the required number $(xy)$is 57.

Note: If the required number is xy then the value of xy is equal to (10 times x + y). When we reverse the digits we get yx, the value of yx is similarly (10 times y + x).

Let the required number is xy, that means ten’s place of the digit of required number be x and the units place of the digit be y. Then,

$x + y = 12$ ..... (1)

Required Number =$\left( {10x + y} \right)$.

After interchanging the digits number will be$(10y + x)$.

Given that the number formed by interchanging the digits of the original number exceeds the original number by 18.

$ \Rightarrow \left( {10y + x} \right) - (10x + y) = 18$

$ \Rightarrow 9y - 9x = 18$

$ \Rightarrow y - x = 2$ ..... (2)

On adding equations (1) and (2), we get

$\eqalign{

& 2y = 14 \cr

& \Rightarrow y = 7 \cr} $

Therefore, $x = 12 - 7 = 5$

Hence the required number $(xy)$is 57.

Note: If the required number is xy then the value of xy is equal to (10 times x + y). When we reverse the digits we get yx, the value of yx is similarly (10 times y + x).

Last updated date: 22nd Sep 2023

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