Question

U 14 = 27 mempe
A number consists of two digits whose sun is 9. If 9
is subtracted from the number, its digits are interchanged
Find the number.​

Answer 1

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A number consists of two digits whose sum is 9. If 9 is substracted from the number, its digits are interchanged . Find the number.

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• A number is made up of two digits whose sum is 9.

• If 9 is substracted from the number, it's digits are interchanged.

$\\ \huge \mathfrak { \underbrace\purple{to \: find}\pink\leadsto}$

• The number = ?

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$\large\sf \: let, \\ \large \sf the \: digits \: at \: once \: place \: be = x \\ \large \sf \: the \: digit \: at \: tens \: place \: be \: = 9 - x \\ \\ \large \sf\therefore \: the \: number \: is \\ \longrightarrow \large\sf 10(9x - x) + x = 90 - 10x + x = 90 - 9x \\ \large \sf \: now \: by \: reversing \: the \: number \: the \: new \: no. \: obtained \: is \\ \large \sf 10x + 9 - x = 9x + x \\ \\ \large \sf \: (as \: mention \: in \: the \: question \: that \: if \: 9 \: is \: substracted \: with \: the \: no. \: the \: digits \: are \: interchanged)$

➲90-9x-9=9x+9

➲81-9x=9x+9

81-9=9x+9x

18x=72

x=72/18

x=4

digits at ones place is x=4

tens place=9-x=9-4=5

Thus the number is 54