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Ages and ages (Posted on 2003-11-04) Difficulty: 2 of 5
A Father, son and grandson are walking in the park. A man approaches them and asks for their age. The Father replies, "My son is as many weeks as my grandson is in days, and my grandson is as many months old as I am in years. We are all 100 years together."

How old were each?

  Submitted by Popstar Dave    
Rating: 3.6667 (6 votes)
Solution: (Hide)
Let f, s and g be the ages in years, of the father, son and grandson, respectively.

As I know that you're all going to get technical on me, I'll use 6 d.p. for my calculations.
In a year there are technically 365.242199 days.
This leaves us with 52.177457 weeks.
Months are fixed at 12.
(note: this also works if you use 365 and (365/7) for days and weeks, respectively.)

Age of the son in weeks is the same as the age of the grandson in days:
52.177457*s = 365.242199*g

Age of the grandson in months is the same as the age of the father:
12g = f

Sum of their ages is 100 years:
f + s + g = 100

Solving these, we get:
s = (365.242199/52.177457)*g
= 7g
and
f = 12g

Therefore:
12g + 7g + g = 100
20g = 100
g = 5

s = 7g
s = 35

f = 12g
f = 60

The father is 60 years old, the son is 35 years old and the grandson is 5 years old.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle Solution With ExplanationK Sengupta2007-04-27 14:41:30
Some ThoughtsProblem SolutionK Sengupta2007-04-27 14:40:48
SolutionSolutionTimothy2004-03-26 23:52:27
Some Thoughtsre: SolutionDan2003-11-05 20:00:40
SolutionLee2003-11-05 00:05:41
how many days in a monthjaypee2003-11-04 21:39:26
Anomolie?Chaz2003-11-04 19:22:21
SolutionSolutionS2003-11-04 15:33:36
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