SOLUTION: A man lived a fourth of his life as a boy, a fifth as a young man and a third as an adult. He spent 13 years in his old age. How old was he when he died?

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Question 114792: A man lived a fourth of his life as a boy, a fifth as a young man and a third as an adult. He spent 13 years in his old age. How old was he when he died?
Found 2 solutions by Fombitz, ganesh:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Life as a boy + Life as young man + Life as adult + Life in old age=Whole life
1%2F4%2B1%2F5%2B1%2F3%2BO=1
Where O is the fraction of his life spent in old age.
60%2A%281%2F4%2B1%2F5%2B1%2F3%2BO%29=60 Multiply both sides by 60 (4*5*3) to remove fractions.
15%2B12%2B20%2B60%28O%29=60
60%280%29=13
O=13%2F60
The man spent 13/60 of his life in old age.
His total years in old age equals 13 years.
%2813%2F60%29A=13
A=60
The man was 60 years old when he died.

Answer by ganesh(20) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the age when the man died.
Then (1/4)x + (1/5)x + (1/3)x + 13 = x ( Since, a fourth of his life was lived as a boy can be written as (1/4)x.
Solve the above equation.
(1/4)x + (1/5)x + (1/3)x - x = -13
(1/60){15x +12x + 20x - 60x}= -13 ( Take LCM)
-13x = -780
x = 60.
The age of death is 60