Grandpa Age

Q. 
Grandpa:

"My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 100 years. Can you tell me my age in years?"


Ans. Grandpa:

"This problem is conveniently solved by writing down the necessary equations. Note that there are 12 months in a year, 52 weeks in a year, and 365 days in a year.

Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,

365g = 52s.

Since my grandson is 12g months old,

12g = m.

Since my grandson, my son and I together are 100 years,

g + s + m = 100.

The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows.

m / 12 + 365 m / (52 × 12) + m = 100 or

52 m + 365 m + 624 m = 624 × 100 or

m = 624 × 100 / 1041 = 60.

So, I am 60 years old."

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