Question

In a two digit number ,the unit's digit is twice the ten's digit .if 27 is added to the number, the digits interchange their places.the number is

Answer 1

Answer:

so, the number is 36. because let the no. is 10y + x.

Answer 2

$\underline\mathfrak{Given:-}$

• $\: \: \: \: \: \small\sf{In \: \: a \: \: two \: \: digit \: \: number, \: \: the \: \: unit's \: \: digit. \: \: is \: \: twice \: \: the \: \: ten's \: \: digit.}$
• $\: \: \: \: \: \small\sf{If \: \: {27} \: \: is \: \: added \: \: to \: \: the \: \: number, \: \: the \: \: digits \: \: interchange \: \: their \: \: places.}$

$\underline\mathfrak{To \: \: Find:-}$

• $\: \: \: \: \: {find \: \: the \: \: number.?}$

$\huge\underline\mathfrak{Solutions:-}$

• $\: \: \: \: \: \: \: {Let \: \: the \: \: ten's \: \: digit \: \: be \: \: x}$

• $\: \: \: \: \: {so \: \: unit \: \: digit \: \: will \: \: be \: \: 2x}$

$\: \: \: \: \: {so \: \: the \: \: number \: \: {10x} \: + \: {2x} \: \: = \: \: {12x}}$

$\underline\mathfrak{According \: \: to \: \: questions:-}$

$\: \: \: \: \: {Now, \: \: if \: \: the \: \: number \: \: if \: \: 27 \: is \: \: added \: \: to \: \: the \: \: number \: \: the \: \: digits \: \: interchange \: \: their \: \: place.}$

$\: \: \: \: \: \leadsto \: \: {x}^{2} \: - \: \frac{6x}{5} \: + \: \frac{9}{25} \: \:= \: \: \frac{2}{5} \: \: + \: \frac{9}{25}$

$\: \: \: \: \: \leadsto {12x} \: + \: {27} \: \: = \: \: {21x}$

$\: \: \: \: \: \leadsto {27} \: \: = \: \: {21x} \: - \: {12x}$

$\: \: \: \: \: \leadsto {27} \: \: = \: \: {9x}$

$\: \: \: \: \: \leadsto {x} \: \: = \: \: \frac{27}{9}$

$\: \: \: \: \: \leadsto {x} \: \: = \: \: {3}$

$\: \: \: \: \: {Thus, \: \: the \: \: ten's \: \: place \: \: digit \: \: is \: \: 3.}$

$\: \: \: \: \: \underline{Find \: \: the \: \: numbers.}$

$\: \: \: \: \: \leadsto {2x} \: \: = \: \: {2} \: × \: {3}$

$\: \: \: \: \: \leadsto {2x} \: \: = \: \: {6}$

$\: \: \: \: \: \leadsto {x} \: \: = \: \: {30} \: + \: {6}$

$\: \: \: \: \: \leadsto {x} \: \: = \: \: {36}$

$\: \: \: \: \: {So, \: \: the \: \: required \: \: number \: \: is \: \: {36}.}$

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