The ages of Old and Young total 48. Old is twice as old as Young was when Old was half as old as Young will be when Young is three times as old as Old was when Old was three times as old as Young.
How old is Old ?
Old is now 30, and Young is 18.
To see this, let: Ot = Old's age today
Yt = Young's age today
Ya = Young's age when Old was three times as old as Young
Oa = Old's age when Young was Ya
and d = difference in Old's and Young's ages.
Then Ot + Yt = 48
Ot = Yt + d
so Ot + (Ot - d) = 48 (I)
The difference between Old's and Young's ages at all times is d, so the result of the convoluted statement is:
Ot = 2 * (9/2 * Ya - d)
Ot = 9*Ya - 2*d (II)
Now Oa = Ya + d = 3* Ya, so Ya = d/2
Substituting for Ya in (II) we get
d = 2/5 * Ot
Substituting for Ot in (I),
Ot + Ot - (2/5 * Ot) = 48
Ot = 30
Yt = 18
and Ya = 6.
The convoluted statements says that 30 is twice the age Young was when Old was 27. At that time, Young was 15.
solution
