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