Diophantus Confuses You

Algebra Level 2

Life of Famous Greek Mathematician, Diophantus is described as a puzzle below :

He was a boy for 1/6 of his life. After 1/12 more, his beard grew. After another 1/7, he married. In fifth year after his marriage, he was blessed with a son. The son lived half as many as his father. Diophantus died 4 years after his son. What was the age of Diophantus when he died ?

84 81 74 85

Anish Harsha by Anish Harsha , 20, India

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4 solutions

Yashraj Jariwala
Feb 10, 2015

Let the age of Diophantous be x when he died Thus,age of son when he died is 1/2x Therefore, 1/6x+1/12x+1/7x+5+1/2x+4=x, So,25/28x+9=x So,3/28x=9 So,x=84 Thus,age of diophantous was 84 when he died.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I cheated by looking for the age which had the denominators (6,12 & 7) as factors since his age had to be an integer

Zx Yeoh - 6 years, 4 months ago
Refath Bari
Feb 23, 2015

Find the LCM of 7,6,and 12,and you get the answer.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Caleb Townsend
Feb 14, 2015

Note his final age must be divisible by 6 , 12 , and 7. 6,\ 12,\ \text{and}\ 7. Divisibility by 12 12 implies divisibility by 6 , 6, so the least satisfactory number is 12 × 7 = 84. 12\times 7 = 84.
Furthermore note that his age must have been even, since his son's age was half his. Since 84 84 does not contradict these, it is the correct answer.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Hasmik Garyaka
Sep 15, 2017

I solved this problem when I was 5th grade. When it was?

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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