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Old Man Wrinkle

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Man Wrinkle spent one-fourth of his life as a boy, one-eighth as a youth, and one-half as an active man. If Man Wrinkle spent 9 years as an old man, then how many years did he spend as an active man?
Answer: 36

Solution:

Fraction of life as a boy = 1/4
Fraction of life as a youth = 1/8
Fraction of life as an active man = 1/2
Fraction of life as boy, youth and active man = 1/4 + 1/8 + 1/2 = (2 + 1 + 4)/8 = 7/8
Fraction of life as an old man = 1 − 7/8 = 1/8
Thus, one-eighth of Man Wrinkle's life (as an old man) is 9 years.
So, Man Wrinkle's Age = 72 years.

It may be noted that:
Life as boy = 72/4 = 18 years.
Life as youth = 72/8 = 9 years.
Life as active man = 72/2 = 36 years.
Life as old man = 72/8 = 9 years.

The problem may also be solved by setting up the following equation: a/4 + a/8 + a/2 + 9 = a
where a denotes Man Wrinkle's age in years.
The equation may be solved as shown below.
7a/8 + 9 = a
9 = a − 7a/8 = a/8
a/8 = 9 or a = 72.

Therefore, life spent as active man = 72/2 = 36 years.

Food for thought:

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