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Grandfather's Age

Puzzle:

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years?


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Solution:

I am 72 years old.

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 120 years,
g + s + m = 120.
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 = 120 or
52 m + 365 m + 624 m = 624 x 120 or
m = 624 x 120 / 1041 = 72.
So, I am 72 years old.

4 comments:

Ankit Goswami said...

72

Sabari said...

I + S + GS = 120
I = 12GS
S = 7GS

... I = 72, S = 42, GS = 6

Naresh said...

grand son -6
father-42
grand father-72

Rajiv Gupta said...

Easy
Suppose GS is x yrs old; then
Son (y)= 7x yrs.
self (z) = 12x yrs.
x+y+z=120
Substitute values of y & z from above;
x + 7x + 12x =120; or
20x = 120; x = 6
GS 6 yrs.
Son 6*7, 42 yrs.;
Self 6*12, 72 yrs. old