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 ?
(In reply to
Puzzle Answer by K Sengupta)
We denote:
Op = Old's present age.
Yp= Young's present age.
Yg= Young's age when Old was three times as old as Young.
Og= Old's age when Young's age was Yg.
d= Difference between Old's and Young's present ages.
Then, we have:
Yp=Op-d
Op+Yp=48
=> Op+Op-d = 48
=> 2*Op - d = 48 ..........(I)
The difference between Old's and Young's ages remains constant at d.
Therefore the given conditions yield:
Op = 2*{3*(3/2) * Yg -d}
= 9*Yg - 2d ........(II)
Also, we have:
Og= 3*Yg
=> 3*Yg = Yg +d
=> Yg=d/2 ......(III)
Substituting (III) in (II), we have:
Op = (5/2)*d
=> d = (2*Op)/5
Again, substituting this in (I), we have:
2*Op - (2*Op)/5 = 48
=> (8*Op)/5 =48
=> Op = 30 => d=(2*30)/5= 12
=> Yp = 30-12 =18
also, Yg = d/2=12/2 = 6
and, Og = 3*6=18
Thus the respective present ages of Old and Young are 30 and 18.
Edited on September 12, 2022, 12:19 am
Explanation for Puzzle Answer
