Question

The digit at the ten's place of a two digit number is four time than its unit place. If the digit are reversed than the new number will be 54 less than the original number. Find the original number.

Answer 1

Let the two digits of no. be x and y.
The no. will be 10x+y
x=4y
x-4y=0..........(1)
10x+y-10y-x=54
9x-9y=54
x-y=6
x-y-6=0..........(2)
From (1) and (2), 
x -4y+0=0
x - y-6=0


On eliminating x, we get y=2, and x=4y=8.
Hence the original no, is 82.

Answer 2

Let the digit at unit's place = x
 Then the ten's digit =4x

 original no =10(4x)+x
                     =41x
  reversed no =10(x)+4x
                     =14x
               ATQ
   41x=14x +54
    27x =54
  x=2

no=10(4x)+x
    =10(4×2)+2
     =80+2
     =82         Hope You Understand . Good Luck