Fractions of remainders
How to find the total when a series of fractions of the total and fractions of remainders were given in a will? The key is to use portions in the fractions.
The Puzzle of the Eccentric Will in Fractions of Remainders
In the will of an eccentric millionaire, he left 4/17th of his estate to his son, 7/13th of the remainder to his wife, 2/3rd of this remainder to his daughter and the remaining $2 million to his dog. What was the total value of his estate and who got most?
You cannot use any mathematical variable and equations.
Solution thoughts
Will you calculate the first remainder as a fraction of the total? But then, you have to use of course a mathematical variable for the unknown total which you cannot do by the puzzle condition.
We will then ignore the value of the total altogether (naturally, we have to find it, isn't it?). We will instead concentrate on the 4/17th of his estate given to his son.
If 4 out of 17 portions of his estate was given, then we can very well assume his estate to be of 17 portions without bothering about the value altogether. For now.
First gift
4 out of 17 portions he gave to his son. Remaining was 13 out of total 17 portions.
Second gift
7/13th of the remainder was given to his wife. If 13 portions were the remainder, 7 of this was given to his wife. Remaining now 6 portions (of total 17 portions).
Third gift
2/3rd of this remaining was given to his son. Two third of 6 would be 4. So his son got 4 portions of the remaining 6. Now left is 2 portions of the total.
Fourth gift
This remaining amount of value $2million was left to his dog.
If 2 portion value were $2 million, 17 portions of his estate value must be $17 million.
Who got most? It must be his wife.
Food for thought
We have not used any variable or mathematical equation. Instead, we have used the most basic concept of a fraction, say 4/17th, as 4 out of 17 portions.
A fraction actually doesn't have any unit. It shows only portions.
This very basic portions concept of fractions can be used very effectively in lightning fast solution of MCQ type fraction problems appearing in top competitive exams.
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