Eight years ago Farhan's age was half his sister's age. Today their ages add up to 52 years. How old is Farhan today?

Let Farhan be $f$ and his sister $s$ today. Eight years ago $f-8=(s-8)/2$, so $2f-16=s-8$ and $s=2f-8$. With $f+s=52$, we get $f+2f-8=52$, so $3f=60$ and $f=20$ (his sister is 32). Check: eight years ago they were 12 and 24. 32 is the sister'$s$ age. 26 splits the 52 evenly, ignoring the older sister. 12 is Farhan'$s$ age eight years ago, the figure the halving condition actually describes.