Question

in two digit umbwers ,the sum of digits is 13 .if the number is subtracted from the one obtained by interchanging the digits.the result is 45 .what is the numbers.

Answer 1

let two digit number be 10x + y and it's reverse number be 10y + x

the sum of digits is 13
so, x + y = 13
x = 13 - y..........(1)

the number is subtracted from the one obtained by interchanging the digits is 45
so, 10x + y - (10y + x) = 45
10x + y - 10y - x = 45
9x + 9y = 45
9(x - y) = 45
x - y = 5............(2)

substitute (1) in (2)
so, (13 - y) - y = 5
13 - 2y = 5
2y = 13 - 5
2y = 8
y = 4

substitute y in (1)
x = 13 - 4
x = 9

so, two digit number is 10x + y = 10×9 + 4 = 90 + 4 = 94 and
it's reverse digit is 10y + x = 10×4 + 9 = 40 + 9 = 49

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