Old Man Wrinkle puzzle

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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?

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    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.

    anikam Expert Answered on 20th August 2015.
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