Question

A number consists of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.

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Hint : If the number is ab it can also be written as 10a+b since a is at tens place and b is at ones place.

Let the digits at the tens place be x and ones place be y.
Hence the number is 10x + y ……(i)
By reversing the number it becomes 10y + x ……(ii)
According to the question we have
x + y = 5 ……(iii)
Also when 9 is added to the number the digits get interchanged.
$10x + y + 9 = 10y + x \\ 9x - 9y + 9 = 0\, \\$
$y - x = 1\,\,\,$ ……(iv)
$2y = 6 \\ y = 3 \\ \\$ (v)