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 - 9*x** * ...........(1)

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

according to the given condition,

(90 - 9*x*) - (9*x* + 9) = 27

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

- 18*x* = - 54 ⇒ *x* = 3

so from (1), we get

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

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