Question

the sum of two digits of a two digit number is 12 if the digits are reversed then the number so formed exceeds the original number by 18 find the original number

Answer 1

Answer:

x = 14/11 and y = -8/11

Step-by-step explanation:

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Answer 2

Answer:

$\boxed{\sf \: Number \: = \: 57 \: }$

Step-by-step explanation:

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{digit \: at \: ones \: place \: be \: y} \\ \\ &\sf{digit \: at \: tens \: place \: be \: x} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{Number \: formed \: = \: 10x + y} \\ \\ &\sf{Reverse \: number \: = \: 10y + x} \end{cases}\end{gathered}\end{gathered}$

According to statement, sum of the digits of a two digit number is 12.

$\sf \: x + y = 12$

$\sf\implies \sf \: y = 12 - x - - - (1)$

According to statement, the reverse number exceeds the original number by 36.

$\sf \: 10y + x - (10x + y) = 18$

$\sf \: 10y + x - 10x - y = 18$

$\sf \: 9y - 9x= 18$

$\sf \: 9(y - x)= 18$

$\sf \: y - x = 2$

On substituting the value of y from equation (1), we get

$\sf \: 12 - x - x = 2$

$\sf \: 12 - 2x = 2$

$\sf \: - 2x = 2 - 12$

$\sf \: - 2x = - 10$

$\sf\implies \sf \: x = 5$

On substituting the value of x = 5 in equation (1), we get

$\sf\implies \sf \: y = 12 - 5 = 7$

Hence,

$\sf \: Number \: \: = \: 10 \times 5 + 7$

$\sf\implies \bf \: Number \: = \: 57$