What are their ages in years?
The grandson is about as many days old as the son is in weeks. The grandson is approximately as many months old as the father is in years. The ages of the grandson, the son, and the father add up to 120 years. What are their ages in years?
Let G, S, and F represent the ages in years of the grandson, the son, and the father, respectively. Since a year has 365 days, or 52 weeks, or 12 months, the problem can be represented by three equations with three unknowns:
365 G = 52 S (The grandson is about as many days old as the son is in weeks)
12 G = F (The grandson is approximately as many months old as the father is in years)
G + S + F = 120 (The ages of the grandson, the son, and the father add up to 120 years)
Because the grandson’s age is G = F/12, the son’s age can be represented in terms of F by substituting:
S = (365/52)×G
S = (365/52)×(F/12)
The third equation can now be represented with only the father’s age as an unknown:
F/12 + (365/52)×(F/12) + F = 120
Multiplying by 12, we get:
F + (365/52)×F + 12 F = 120×12
20 F = 1440
F = 72
G = F/12 = 6
S = (365/52)×6 = 42
The father is 72, the son is 42, and the grandson is 6 years old.
You may have noticed that the statement of the problem is somewhat ambiguous: “The grandson is approximately as many months old as the father is in years” indicates that there may be some variance. A year really has 365 1/4 days instead of 365, and 52 weeks times 7 days gives only 364 days in a year. These inconsistencies produce fractional results that need to be rounded.
Doing the division in the following equation:
F + (365/52)×F + 12 F = 120×12
produces 20.019 F = 1440, which is rounded to 20 F = 1440
Your Answer
More puzzles to try-
Three blue and two red hats puzzle
At a party, four people played a game. Three of them sat one behind the other, so that Abe saw ...Read More »The genders of the neighboring family’s children
The house next door has some new neighbors. They have two children, but you don’t know what mix of boys ...Read More »Which switch belongs to which light bulb?
There are 4 light bulbs in a room and 4 switches corresponding to these four light bulbs (in a random ...Read More »Car Riddle
At a recent motorsport gathering, four proud owners were grouped together around the blue Ferrari, discussing their gleaming sports cars. ...Read More »Behind Stars riddle
I can’t be seen, found, heard or smelled. I lie behind stars and under hills, I fill empty holes, come ...Read More »Six glasses are in a row riddle
Six glasses are in a row. The first three are filled with milk and the last three are empty. By ...Read More »Gets up 180 times
A person gets up 180 times every night and sleeps for at least 7 hours at a time. Where does ...Read More »22 legs and 2 wings
What has 22 legs and 2 wings?Read More »Horse Equation Puzzle
Can you solve the equation by finding the value of A) Horse B) Cowboy boot C) Horseshoe In the Picture?Read More »Howl & Whisper
You can feel it but, it can not feel you. It can uproot trees and tear roofs off. Yet, it ...Read More »Continuously go either up or down in an infinite spiral.
These steps appear to continuously go either up or down in an infinite spiral.Read More »Ladies delight
Metal or bone it may be, many teeth it has and always bared, yet its bite harms no one, and ...Read More »Why Daniel Jumps from the Bridge
Daniel walks into a movie theatre. While in the movie, he suddenly smiles delightfully. About a couple of minutes later, ...Read More »Black and admired
Black he is and much admired, men seek him until they’re tired. When they find him, they break his head, ...Read More »Egg Tale! How is it possible :O
There are six eggs in the basket. Six people each take one of the eggs. How can it be that ...Read More »Famous 5000 Sum trick puzzle
Genuinely write the answer to this sum trick puzzle- “Take a 1000 plus 40 plus 1000 plus 30 plus 20 ...Read More »Always Hungry
He is always hungry, he must always be fed to keep him live, the finger he touch, will soon turn ...Read More »Seam Beam and dream puzzle
If all Seams are Beams and all Beams are Dreams, can all Dreams be Seams?Read More »How will you measure 5 liters
You are given four different jars of 2 liters, 4 liters, 6 liters and 8 liters respectively with an unlimited ...Read More »TV Rebus
What does this Rebus Picture mean?Read More »