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## How Old is Grandpa

Math brain teasers require computations to solve.

 Puzzle ID: #1404 Fun: (2.54) Difficulty: (2.51) Category: Math Submitted By: gokaran

Grandpa says, "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?"

This problem is conveniently solved by writing down the necessary equations.

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 x 12) + m = 100 or

52 m + 365 m + 624 m = 624 x 100 or

m = 624 x 100 / 1041 = 60.

So, I am 60 years old."

Food for thought:

Why is the word "about" used in the Problem Statement in the sentence "My grandson is about as many days as my son is weeks"? Calculate the son's age and the grandson's age. Then, verify whether the first equation (i.e., 365g = 52s) is exactly satisfied.

An elegant solution is possible on realizing the significance of the word "about" in the Problem Statement.

Elegant Solution:

The first equation (365g = 52s) can be approximated by

7g = s.

As before, the other two equations are

12g = m

g + s + m = 100.

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

g + 7g + 12g = 100 or 20g = 100.

m = 12g = 12 x 100 / 20 = 60.

So, Grandpa is 60 years old.

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 cat Dec 12, 2001 neato make more!!!!!!!!!!!!!!!!!!!!! :] pusandave Mar 29, 2002 I am impressed with your ability to explain the answer. It's nice to see it spelled out instead of just "60". paul726 Mar 05, 2006 I agree with liking to see the answer explained, but I don't think so much detail was necessary. tonjawithaj Aug 09, 2006 This one made me think! jasmin215 Oct 29, 2007 WOW! i gave up after i tried it for like 2 mins and after that respose lol gave up even quicker. it sounds right t me since you had a long explain.. must be right good job!!!!!!! javaguru Feb 08, 2009 There is a MUCH easier way to do this--I did this in under 10 seconds in my head. The ratio of ages is 12::7::1. 12+7+1=20. 100/20=5. 5*12=60. This works for all these ratio problems. Setting up equations is a waste of time. Jimbo Apr 15, 2009 If I am x years then my grandson is x/12 years and my son is (x/12)*365/52 which is approximately 7x/12. Thus x + x/12 + 7x/12 = 100 or x = 60. The diffiiculty here is to realise that there are about 7 times as many days as weeks in a year. I like Java's solution better. bookrage Jan 30, 2015 hardest puzzle I've solved to date. I just created an account yesterday but have been coming here for years. Challenging and actually requires a lot more algebra than a lot of stuff here. Liked it. I had to set up the equations to make the problem make sense but did the calculations in my head once I figured out how the problem worked. nice challenge though.