Question

Sum of the digits of a two digit number is 9. When we interchange the digit it is found that the resulting new number is greater than the original number by 27. What is the two digit number

Answer 1

Step-by-step explanation:

$let \: ones \: digit \: be \: x. \\ then \: tens \: digit \: = 9 - x \\ so \: original \: number \: = 10(9 - x) + 1(x) = 90 - 10x + x = 90 - 9x \\ \\ after \: interchanging \: digits \\ ones \: digit \: = 9 - x \\ tens \: digit = x \\ new \: number \: = 10(x) + 1(9 - x) = 10x + 9 - x = 9 + 9x \\ \\ atq \\ original \: number + 27 = new \: number \\ = > 90 - 9x + 27= 9 + 9x \\ = > 18x = 108 \\ = > x = 6 \\ \\ so \: original \: number \: = \: 90 - 9x = 90 - 9(6) = 90 - 54 = 36$

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