Question

A two digit number is such that product of digits is 18 when 63 subtracted from the number the digits interchange their places. Fnd the number. ​

Answer 1

$\blue{\texttt{It is given that}},$

$\blue{\texttt{product of digits }} = 18$

$\blue{\texttt{lets suppose ten's digit}} = x$

$\blue{\texttt{so, the unit digit }}$

$= \Large \frac{18}{x}$

$Number = 10x +\Large \frac{18}{x}$

$we\:can\: get \:number\: \: \blue{\texttt{by inter changing}},$

$= 10x + \Large \frac{18}{x} +x$

$\blue{\texttt{according to the question}},$

$10x +\Large \frac{18}{x}-\Large \frac{180}{x}-x =63$

$= 9x - \Large \frac{162}{x}=63$

$= 9 x^{2}- 63x^{2} - 162 = 0$

$x^{2}-7x -18 = 0$

$x^{2}-9x - 2x - 18 = 0$

$x (x - 9 ) +2 ( x- 9 ) =0$

$(x - 9 ) ( 2 + x) =0$

$x = 9 \:or x =-2$

$\blue{\texttt{now take x = 9}},$

$\blue{\texttt{so , the number is }},$

$10x × 9 +\Large \frac{18}{9}$

$\red{\textbf{ = 92}},$

$\red{\textbf{hence, the number is 92}},</p><p>$