Question

the digit at the tens place of a two digit number is 3 times the digit at the units place if the digits are reversed the new number will be 36 less than the original number find the number

Answer 1

Let the digit in the tens place be x and the digit is the ones place be x

3y = x 
=> -x + 3y = 0            .......i

10x + y - (10y +x) = 36
=> 10x + y - 10x -x = 36
=> 9x - 9y = 36 
taking 9 common, we have 
x - y = 4                    ...............ii

adding i and ii, we get 

  x -   y = 4 
- x + 3y = 0
.....................
0 + 2y = 4
=> y = 4 / 2
=> y = 2

substituting y = 2 in i, we get
3(2) - x = 0
=> 6 - x = 0
=>-x = -6
=> x = 6

Therefore the original number is 36.