The sum of digits of a two digit number is $13$ . If the number is subtracted from the one obtained by interchanging the digits, the result is $45$ . What is the number?

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Solution

The two digit of $2$ -digit number be $x$ and $y .$
$x + y = 13 ⟶ (i)$
$2$ -digit number $= 10 x + y$
$2$ -digit number obtained by reversing the digits $= 10 y + x$
$∴ (10 y + x) - (10 x + y) = 45 \Rightarrow 9 y - 9 x = 45 \Rightarrow y - x = 5 ⟶ (i i)$
On adding $(i)$ and $(i i),$
$2 y = 18$
$y = 9$
Putting $y$ in equation $(i),$ we get $,$
$x + y = 13$
$x = 4$
$∴$ $2$ -digit number $= 10 x + y = 49$

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The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?

The two digit of 2-digit number be x and y.x+y=13⟶(i)2-digit number =10x+y2-digit number obtained by reversing the digits =10y+x∴(10y+x)−(10x+y)=45⇒9y−9x=45⇒y−x=5⟶(ii)On adding (i) and (ii),2y=18y=9Putting y in equation (i), we get,x+y=13x=4∴ 2-digit number =10x+y=49

The sum of digits of a two digit number is $13$ . If the number is subtracted from the one obtained by interchanging the digits, the result is $45$ . What is the number?