Question

a two digit number is 3more than 4times the sum of its digits .if18 is added to this number ,the sum is equal to the number obtained by interchanging the digits . find the number

Answer 1

${ \Huge{ \mathsf{{HEY \: \: THERE!!}}}}$


${ \Huge{ \mathsf{{SOLUTION!!}}}}$



$\implies{ \mathsf{ \tiny{Let \: the \: tens \: \: and \: \: units \: \: Digit \: \: of \: \: the \: \: required \: \: Number \: \: be \: \: x \: \: and \: \: y \: \: respectively!}}}$


$\implies{ \mathsf{ \tiny{Then,}}}$


$\implies{ \mathsf{ \fbox{ \tiny{Required \: Number = \: 10x \: + \: y}}}}$


$\implies{ \mathsf{ \fbox{ \tiny{Original \: \: Number = 10y + x}}}}$





$\implies{ \mathsf{ \fbox{ \tiny{method \: \: of \: \: solution \ratio - }}}}$


$\implies{ \mathsf{ \tiny{10x + y = 4(x + y) + 3}}} \\ \\ \\ \implies{ \mathsf{ \tiny{10x + y = 4x + 4y + 3}}} \\ \\ \\ \implies{ \mathsf{ \tiny{10x - 4x + y - 4y = 3}}} \\ \\ \\ \implies{ \mathsf{ \tiny{6x - 3y = 3}}} \\ \\ \\ \implies{ \mathsf{ \tiny{3(2x - y) = 3}}} \\ \\ \\ \implies{ \mathsf{ \fbox{ \fbox{ \tiny{2x - y = 1 }}}}} \\ \\ \\ \\ \\ \\ \implies{ \mathsf{ \tiny{10x + y + 18 = 10y + x}}} \\ \\ \\ \implies{ \mathsf{ \tiny{10x - x + y - 10y = - 18}}} \\ \\ \\ \\ \implies{ \mathsf{ \tiny{9x - 9y = - 18}}} \\ \\ \\ \implies{ \mathsf{ \fbox{ \fbox{ \tiny{x - y = - 2}}}}} \\ \\ \\ \\ \implies{ \mathsf{ \tiny{on \: subtracting \: (2) \: from \: (1) \: \: so \: we \: get}}} \\ \\ \\ \\ \\ \implies{ \mathsf{ \tiny{value \: of \: x = 3}}} \\ \\ \\ \\ \\ \implies{ \mathsf{ \tiny{substitute \: \: the \: given \: \: value \: \: in \: equation \: \: so \: we \: get}}} \\ \\ \implies{ \mathsf{ \tiny{y = 5}}} \\ \\ \\ \implies{ \mathsf{ \tiny{required \: number \: \: = (10x + y)}}} \\ \\ \\ \\ \implies{ \mathsf{ \tiny{(10 \times 3 + 5)}}} \\ \\ \\ \\ \\ \implies{ \mathsf{ \tiny{ \fbox{35}}}}$





$\implies{ \mathsf{ \fbox{ \tiny{hence \: \: required \: \: number \: \: be \: = 35}}}}$