Question

the sum of the digit of a two digit number is 12 if the new number formed by reversing the digit is greater than the original number by 18 find the original number

Answer 1

Let the tens digit is x and unit digit is y

The number is 10 x + y

10 x + y +18 = 10 y + x

9 x - 9 y = -18

x - y = -2 ………1

x + y = 12….2

2 x = 10 Therefore x =5

From equation 2, 5 + y - 12 Therefore y = 7

The number is 10*5+7= 57

Answer 2

let the unit digit no be =x
the tenth digit be =y
then
10y+x=12
x=12-10y
a/q
10y+x=10x+y
then the transposed
10y-y+x-10x=18
9y-9x=18
then 9 is common
y-x=2
then putting the value of x
y-12-10y=2
-9y-12=2
-9y=14
y=14/-9
then y is =-14/9 then after putting the value of y
x=12-10*14/9
x=-4