Critical Thinking Puzzles: Age problem

December 5, 2008

I am 5 times as old as you were when I was as old as you are.
Find our present ages.

Unknown said...: 18 & 10; December 10, 2008 at 5:28 PM
Anonymous said...: "I" am older than "you" so I > U.

When I was as old as you are now, I - T = U; where T is the time since then. I am now 5 times as old as you were back then so I = 5 * (U - T).

From I - T = U add T to both sides
=> I = U + T. Subst for I in 2nd equation
=> U + T = 5 * (U - T)
=> U + T = 5U - 5T add 5T and subtract U from both sides
=> 6T = 4U

There are an infinite number of values which satisfy these equations, but assuming that the ages and time interval are measured in whole years, the minimum that U can be is 3, with T = 2, and I = U + T = 5.

So I am now 5 and you are 3. 2 years ago I was the age you are now (3) and you were 1. I am now 5 times that age.

These values also work:
U__I__T
6 10 4
9 15 6
12 20 8
etc; December 11, 2008 at 9:23 PM
Anonymous said...: I am 5 times as old as you were when I was as old as you are.

age is i=5X, u=X

i am five times as old as u.I=5U; October 27, 2011 at 8:56 PM
Beca said...: Your 74 wow.; December 16, 2011 at 10:17 PM
Anonymous said...: 5 & 3 is the right answer.

18 & 10 does not satisfy the equation

x = 5 (y-(x-y)); March 18, 2012 at 12:46 AM

Critical Thinking Puzzles