Six years ago Nandini's aunt was five times as old as Nandini. Six years from now the aunt will be twice as old as Nandini. By how many years do their ages differ?

Let Nandini be $n$ and her aunt a today. Six years ago: $a-6=5(n-6)$, so $a=5n-24$. Six years from now: $a+6=2(n+6)$. Substituting, $5n-24+6=2n+12$, so $3n=30,n=10$ and $a=26$. The gap is 26 - 10 = 16 years, and being a gap it is the same at every date: six years ago it was 20 - 4 = 16 and six years from now it will be 32 - 16 = 16. 26 and 10 are the two present ages themselves rather than the gap between them. 24 is the constant in $a=5n-24$, an intermediate value picked up before $n$ was found.