Question

in a two digit number the digit of unit place is double the digit in ten's place the number exeede the sum of digit by 18 then the number is
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Answer 1

$\begin{gathered}\begin{gathered}\bf Given - \begin{cases} &\sf{unit \: digit \: is \: twice \: the \: tens \: digit} \\ &\sf{number \: exceeds \: the \: sum \: of \: digit \: by \: 18} \end{cases}\end{gathered}\end{gathered}$

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$\begin{gathered}\begin{gathered}\bf To \: Find :- \begin{cases} &\sf{the \: number} \end{cases}\end{gathered}\end{gathered}$

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$\large\underline{\bold{Solution :- }}$

$\sf \:  ⟼✬ \: Let \: digit \: at \: tens \: place \: be \: x.$

$\sf \:  ⟼ \: then \: digit \: at \: ones \: place \: be \: 2x$

$\bf \:   ✬ \: Number \: formed \: = \: 10 \times x + 2x \times 1$

$\bf \:   ✬ \: Number \: formed \: = \: 12x - - - - (1)$

✏ According to the statement

☆ Two digit number exceeds the sum of digits by 18

$\bf\implies \:12x - (x + 2x) = 18$

$\bf\implies \:12x - 3x = 18$

$\bf\implies \:9x = 18$

$\bf\implies \:x = 2$

$\begin{gathered}\begin{gathered}\bf Hence :- \begin{cases} &\sf{two \: digit \: number \: = 12x = 12 \times 2 = 24} \end{cases}\end{gathered}\end{gathered}$

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