Question

a two digit number is 4 times the sun of digits and twice of product
digits then find the 2 digit number​

Answer 1

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$\\ \large \sf \: let \: \: 1 \: digit \: \: number \: \: be \: \: \green{ = \sf \: x} \\ \\ \large \sf \: let \: \: 2 \: digit \: \: number \: \: be \: \: \green{ = \sf \: y} \\ \\ \large \underline{\sf hence.} \\ \\ \large\sf \rightarrow \: 2 \: digit \: \: number = 10y + x$

$\large \sf \: given : \\ \\ \large \sf 2 \: digit \: \: number = 4 \: times \: \: sum \: \: of \: \: digits$

$\large \sf \: according \: \: to \: \: question : \\ \\ \large \tt : \implies \: 10 y + x = 4(x + y) \\ \\ \large \tt : \implies \: 10 y + x = 4x + 4y \\ \\ \large \tt : \implies \: 10y - 4y = 4x - x \\ \\ \large \tt : \implies \: 6y = 3x \\ \\ \large \tt : \implies \: \frac{6y}{3} = x\\ \\ \large \tt : \implies \: \frac{ \cancel6 \: \: 2y}{ \cancel3} = x\\ \\ \large \tt \therefore \underline \red{\: x = 2y} \longrightarrow (1)$

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$\\ \large \sf \: given : \\ \\ \large \sf \: 2 \: digit \: \: number = 2 \: timies \\ \large \sf \: product \: \: of \: \: its \: \: digit \\ \\ \large \tt \implies \: 10y + x = 2xy$

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$\\ \large \sf \: dividing \: \: both \: \: sides \: \: by \: \: xy :$

$\large \tt : \implies \: \dfrac{10}{x} + \dfrac{1}{y} = 2 \\ \\ \\ \large \rm \: putting \: \: value \: \: of \: \: x(1) \\ \\ \large \tt : \implies \: \frac{10}{2y} + \frac{1}{y} = 2 \\ \\ \\ \large \tt : \implies \: \frac{ \cancel{10}}{ \cancel2y} + \frac{1}{y} = 2 \\ \\ \\ \large \tt : \implies \: \frac{5}{y} + \frac{1}{y} = 2 \\ \\ \\ \large \tt : \implies \: \frac{6}{y} = 2 \\ \\ \\ \large \tt : \implies \: y = \frac{6}{2} \\ \\ \\ \large \tt : \implies \: y = \frac{ \cancel6 \: \: 3}{ \cancel2} \\ \\ \\ \large \sf \therefore \: \underline \purple{y \: = \: 3}$

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$\\ \large \sf \: putting \: \: values : \\ \\ \large \sf : \implies \: x = 2y = 2(3) = \green6 \\ \\ \large \sf : \implies \:2 \: digit \: \: number \\ \\ \large \sf \: = (10y + x) = 10(3) + 6 = \green{36}$

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