how do you do this question ????

a number consists of 2 digits whose sum is 9.if 27 is subtracted from the number its digits are reversed .find the original number

Let the digit at ones place = x

digit at tens place = 9 - x

original number = 10 ( 9 - x) + x = 90 - 9x    ...........(1)

When the digits are reversed, then new number = 10x + (9 - x) = 9x + 9

according to the given condition,

(90 - 9x) - (9x + 9) =  27 

- 9x - 9x = 9 + 27 - 90

- 18x = - 54 ⇒ x = 3

so from (1), we get

original number = 90 - 9 × 3 = 90 - 27 = 63

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