Question

the sum of the digits of a two digit number is 9 if added if 9 is added to the number formed by reversing the digits then the result is thrice the original number find the original number

Answer 1

$let \: the \: digit \: in \: unit \: place \: be \: x \: \\ tens \: digit \: in \: y \\ \\ x + y = 9 \\ x = 9 - y \\ original \: number \: = 10y + x \\ new \: no = 10x + y + 9 \\ 10x + y + 9 = 3(10y + x) \\ 10x + y + 9 = 30y + 3x \\ 10x - 3x + 9 = 30y - y \\ 7x + 9 = 29y \\ 7x + 9 - 29y = 0 \\ 7(9 - y) + 9 - 29y = 0 \\ 63 - 7y + 9 - 29y = 0 \\ 36y = 72 \\ y = \frac{72}{36} \\ y = 2 \\ hence \: x + y = 9 \\ x + 2 = 9 \\ x = 9 - 2 = 7 \\ \\ so \: original \: number = \\ (10y + x) \: (10) \times (2) + 7 = 27 \\ \\ ans \: is27$

Answer 2

Answer: 27

Step-by-step explanation:

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