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 11 years.
So, Man Wrinkle's Age = 88 years.
It may be noted that:
Life as boy = 88/4 = 22 years.
Life as youth = 88/8 = 11 years.
Life as active man = 88/2 = 44 years.
Life as old man = 88/8 = 11 years.
The problem may also be solved by setting up the following equation:
a/4 +
a/8 +
a/2 + 11 =
a
where
a denotes Man Wrinkle's age in years.
The equation may be solved as shown below.
7
a/8 + 11 =
a
11 =
a − 7
a/8 =
a/8
a/8 = 11 or
a = 88.
Therefore, life spent as active man = 88/2 = 44 years.
Food for thought:
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