Question

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.

Answer 1

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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