math

10x+0.5x +5x +x =99
Solve for x ...or just guess !

Suppose the two digit figure is n while n=10*X+Y:
According "one digit is exactly half the other", there are two possibilities, one is X=2*Y; the other: Y=2*X
"If the position of both fonts or digits is interchanged", then the figure becomes m while m=10*Y+X
"the resultant figure when added with the origional figure sum to 99" means n+m=99, that is (10*X+Y) + (10*Y+X)=99
We can get two combinations:
The first: X=2*Y, and (10*X+Y) + (10*Y + X)=99
The second: Y=2*X, and (10*X+Y)+(10*Y+X)=99
The first condition, X=6 and Y=3, then n=10*X+Y=10*6+3=63
The second condition, X=3 and Y=6, then n=10*X+Y=10*3+6=36