Question

Q.=) The sum of the digit of a 2- digit number is 6. If the digits of the number are reversed, the new number is decreased by 36. Find the number?​

Answer 1

Step-by-step explanation:

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Answer 2

★ Assume :

$the \:number = 10x + y\\ \\ \\so\: the\: reverse = 10y + x$

★ Given :

$x + y = 6...(1)\\ \\ \\(10x + y) - (10y + x) = 36$

★ Solution :

$10 x + y -10y - x = 36\\ \\ \\(10x-x) + (y-10y) = 36\\ \\ \\9x -9y = 36\\ \\ \\ 9(x-y) = 36$

$x - y = \frac{\cancel{36}}{\cancel{9}} \\ \\ \\ x -y = 4 .......(2) \\ \\ \\ (1)+(2) \\ \\ \\ x+\cancel{y} + x - \cancel{y} = 6+4 \\ \\ \\ 2x = 10 \\ \\ \\ x = \frac{10}{2} \\ \\ \\ x = 5 \\ \\ \\ x+y = 6 \\ \\ \\ 5+y = 6 \\ \\ \\ y = 1 \\ \\ \\ number = 10x+y = 50 + 1 \\ \\ \\ {\pink{\boxed{\therefore \: required\: number = 51}}}$