# Puzzle | Luxury Cars

• Difficulty Level : Medium
• Last Updated : 30 Nov, 2017

A father wants to divide his 17 luxury cars among his three sons. According to the father, the oldest son should get half of the luxury cars, the middle son should get one third of the luxury cars and the youngest son should get one ninth of the luxury cars. When the father died, his sons were not able to divide the luxury cars as the result was coming in fractions. As the sons were fighting on how to divide the luxury cars, a traveling mathematician driving by his luxury car came and heard their problem. He proposed a solution with which all the sons got their share in the property without destroying any car.
What was the advice given by the traveling mathematician and how the group of luxury cars was divided?

Solution:
Well, this puzzle is interesting. You have to think such that with the solution everybody is happy and nobody suffer any loss.
Let’s see the problem first.
We have 17 luxury cars to be divided among three sons with the ratio as given in the problem statement.
1st son — half of the luxury car (17 / 2) = 8.5
2nd son — one third of luxury car (17 / 3) = 5.66
3rd son — one ninth of luxury car (17 / 9) = 1.88

As we can see all the results are in fraction so the luxury cars cannot be distributed like this. What will the traveling mathematician do to solve it.
It’s simple. The traveling mathematician adds his luxury car to the group of luxury cars. So in total we have 18 luxury cars now. Now let’s see the scenario again.
1st son — half of the luxury car (18 / 2) = 9
2nd son — one third of luxury car (18 / 3) = 6
3rd son — one ninth of luxury car (18 / 9) = 2

So in total 17 luxury cars will get distributed among the three sons and the traveling mathematician will take his luxury car and leave. 🙂

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