Sum of the digits of a two digit number is 9. When we interchange the digits of the two digit number, the resultant number exceeds the original number by 27. Find the number.

Given :

Sum of the digits of a two digit number = 9

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

To do :

We have to find the original number.

Solution :

 Let the two digit number be $10x+y$.

$x + y = 9$

The number formed on reversing the digits is $10y+x$.

Therefore,

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

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

$9(y-x) = 27$

$y-x = 3$

$y-(9-y) = 3$

$y+y = 3+9$

$2y = 12$

$y = 6$

$x = 9-6 = 3$

The original number is $10(3)+6 = 30+6 = 36$.

The original number is 36.

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Updated on: 10-Oct-2022

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