Three years ago Meena's father was seven times as old as Meena. Nine years from now he will be three times as old as her. What will their two ages add up to at that future date?

Let Meena be $m$ and her father $f$ today. Three years ago: $f-3=7(m-3)$, so $f=7m-18$. Nine years from now: $f+9=3(m+9)$. Substituting, $7m-18+9=3m+27$, so $4m=36,m=9$ and $f=45$. Check both snapshots: three years ago they were 42 and 6, and $42=7\times 6$; nine years from now they will be 54 and 18, and $54=3\times 18$. Those two future ages add to 54 + 18 = 72 years. 63 takes today's total of 54 and adds 9 just once, but BOTH of them age over those nine years, so the total climbs by 18. 54 is what their ages add to today, not at the future date. 18 is Meena's age at that date, one person instead of two.