The sum of digits of a two digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find number.

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Solution

Let the units digit be x and tens digit be y.
Then, $x + y = 15$ ……….(i)
Given number: $10 y + x$
Interchanged digits: $10 x + y$
A.t.Q:-

$\Rightarrow (10 x + y) - (10 y + x) = 9$

$\Rightarrow 10 x + y - 10 y - x = 9$
$\Rightarrow 9 x - 9 y = 9$

$\Rightarrow x - y = 1$ ………(ii)
Solving (i) and (ii)

$x = 8$ , $y = 7$

$∴$ Two digit number $= 78$ .

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The sum of digits of a two digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find number.

Let the units digit be x and tens digit be y.Then, x+y=15 ……….(i)Given number: 10y+xInterchanged digits: 10x+yA.t.Q:-⇒(10x+y)−(10y+x)=9⇒10x+y−10y−x=9⇒9x−9y=9⇒x−y=1 ………(ii)Solving (i) and (ii)x=8, y=7∴ Two digit number=78.