A two digit number is 3 …

Let  us suppose that the ten's digit of required number be x and its unit digit be y respectively.
Therefore, required number = 10x + y
According to the given conditions
10x + y = 4(x + y)  + 3
{tex} \Rightarrow{/tex} 10x + y = 4x + 4y + 3

or, 10x +y - 4x - 4y = 3
{tex} \Rightarrow{/tex} 6x - 3y = 3
{tex} \Rightarrow{/tex} 2x - y = 1...........(i)
and
10x + y + 18 = 10y + x

{tex}\Rightarrow{/tex}10x + y - 10y - x = - 18
{tex} \Rightarrow{/tex}9x - 9y = -18
{tex} \Rightarrow{/tex}9(x - y) = -18
{tex} \Rightarrow ( x - y ) = \frac { - 18 } { 9 }{/tex}
{tex} \Rightarrow{/tex}x - y = - 2   .........(ii)
Subtracting equation (ii) from equation (i), we get

x - y - ( 2x - y) = - 2 - 1

x - y - 2x +y = - 3

- x = -3
{tex} \therefore{/tex}x = 3
Put the value of x = 3 in equation (i), we get
2{tex} \times{/tex}3 - y = 1
{tex} \Rightarrow{/tex}y = 6 - 1 = 5
{tex} \therefore{/tex} x = 3, y = 5
Required number = 10x + y
= 10 {tex} \times{/tex}3 + 5
= 30 + 5
= 35
Therefore the  required number is 35.