Question

a number is atwo digit number which is three times more than 4 times the sum of the digits . if 18 is added to the number , the digits gets opposite. represent geometrically.

Answer 1

let one digit be 'x'

let another digit be 'y'

let two digit = 10x + y because :-
{for example if we take 26 then 26 = 10(2) + 6}

according to question

10x + y = 3 + 4(x + y)

=>10x + y = 3 + 4x + 4y

=>6x - 3y = 3

=3(2x - y) = 3

=>2x - y = 1______eq1

(If 18 is added to number. number get reversed!)
then,

18 + 10x + y = 10y + x

=>9x - 9y = -18

=>9(x - y) = -18

=>x - y = -2_______eq2

eq1 - eq2
x = 1-(-2) = 3

put x =3 in eq2
3 - y = -2
y = 3+2 = 5

We got x as 3 & y as 5

so 10x + y = 10(3) + 5

=>30 + 5 = 35

so two digit number is 35


● for geometrical representation, draw a number line and mark 35 and 53 in it. And measure distance between 35 and 53 as 18.