July 9, 2009

The ultimate age problem

Varun is 33 years old. This is three times as old as Tharun was when
Varun was as old as Tharun is now...

How old is Tharun now ?

Damien said...

He's 22 years old. Anonymous said...

Right. Anonymous said... Secret Squïrrel said...

(Explanation for anonymous)

This problem is simple enough for you to work out the answer by trial and error or plugging values into a spreadsheet but I used algebra.

Varun is 33 now. Call that Vn (ie Vn=33). It's 3 times as old as Tharun was, when Varun was the age that Varun is now.

So at some time in the past Tharun was 33/3 = 11. Call this Tp (Tp=11).

Tharun's age now (call it Tn) is not known but the second sentence tells us that Varun was this age at the same time in the past as when Tharun was 11.

So Tn=Vp. Since the same amount of time has elapsed for both between the past time and now, we also know that Vn-Vp = Tn-Tp (their ages now minus their ages back then gives the amount of time that has elapsed which must be the same for both).

Plug in the known values and it becomes:

33-Vp = Tn-11

Add 11 to both sides:
44-Vp = Tn

Normally, with two unknowns (Vp and Tn) we would not be able to solve this equation, but we know that Vp is the same as Tn (Tn=Vp from above)so:

44-Tn = Tn

Add Tn to both sides
44 = 2*Tn
22 = Tn

Thus Tn (Tharun's age now) is 22

Hope that helps.