# A two digit number is four times the sum of its digits. If 27 is added to the number the digits are reversed, find the number.

Let the 2 digit number be in the form of 10x+y where x and y intergers.

so according to question
10x+y= 4(x+y)

10x+y=4x+4y
6x-3y=0
2x-y=0 ......... (i)

And If 27 is added to the number the digits are reversed

So

10x+y+27=10y+x
9x-9y +27= 0
x-y+3=0  .......................(ii)

substracting (ii) from (i) we get

2x-y-x+y-3=0
So x = 3

similarly y=6

So the number is 36

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