The sum of the digits of a two digit number is 7. If the number formed by reversing the digits is less than the original number by 27, find the original number.
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Let the two digit number be 10x + y, where x > y, then the two digit number with digits reversed will be 10y + x, which is less than the original.
Given that the sum of digits is 7, i.e.,
x + y = 7 → (1)
and the difference between the two digit numbers is 27, i.e.,
(10x + y) - (10y + x) = 27
10x + y - 10y - x = 27
9x - 9y = 27
9(x - y) = 27
x - y = 3 → (2)
On adding (1) and (2), we get,
x = 5
and on subtracting (2) from (1) we get,
y = 2
Hence the two digit number is 52.
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