Fathers And Sons

Number Theory Level 4

Three family members are eating in a restaurant, a grandfather, a son & a grandson. A waiter asks her boss for the ages of her three customers. The boss replied: "The product of their ages is 4032. The grandfather's age divided by grandson's age is twice your age & the sum of their ages is twice of my age too". How old is the son?

All ages are integers.


The answer is 28.

Allan Baguio by Allan Baguio , 61, Philippines

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1 solution

Allan Baguio
Mar 19, 2014

Grandfather is 72y.o.,son is 28 y.o. grandson is 2 y.o.Whereas the waiter is 18y.o. & the boss is 51 y.o.

Sum of the ages= 102 which is twice of 51 Product= 4032 grandpa's age divided by grandson's age = 72/2 which is 36 &twice of 18

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you explain how someone can arrive at this conclusion? In particular, why is that the unique solution?

It's easy to show that the set of numbers you started off with satisfies the conditions. It's much harder to explain how to work from the conditions to arrive at the set of numbers.

Calvin Lin Staff - 7 years, 2 months ago

The problem is incorrect i found many solutions to the above problem one of the possible solution is that grandfather is 84 years old, son is 24 years old and grandson is 2 years old the product of 84X24x2= 4032 sum of ages of son ,grandson,grandfathers age is = 110 (twice of 18) grandfathers age divided by grandson's age = 42 (twice of 21)

Harsh Depal - 7 years, 2 months ago

Insufficient information and poor clarity in the problem. With the only condition that the ages must be integers, there are other possible solutions like 21 and 24 for the son's age which will satisfy the conditions. From the problem the meaning conveyed is that the sum of the ages of GF and GS is twice the age of the boss, but the author has meant the sum of all 3 ages is twice the age of the boss. Please be careful while framing the problems. I wonder how the problem has been categorized as level 4 without even noticing the serious handicap in it....

Harisree Krishnamoorthy - 7 years, 2 months ago

please prove it ..

Vighnesh Raut - 7 years, 2 months ago

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