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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