a number of two digits exceed by 9 the number form by reversing the digit. If the sum of the digits is 13.find the numbers

Let the 2 digit number be 10a + b, where a and b are the tens digit and the ones digit.

Given that

a + b = 13 (equation 1) and

10a + b —9 = 10b + a (equation 2)

So 9a = 9b + 9 , which means

a = b + 1 (equation 3)

Substitute (3) into (1)

(b + 1) + b = 13

2b = 12

b = 6 (equation 4)

Substitute (4) into (3)

a = 6 + 1 = 7 (equation 5)

The 2 digit number is 76.
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