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A man is 42 years old and his son is 12 years old. In how many years will the age of the son be half the age of the man at that time?

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#### Solution

Man’s age = 42 years

Son’s age = 12 years

Let after x years the age of the son will be half the age of the man.

Man’s age after x years = (42 + x) years

Son’s age after x years = (12 + x) years

According to the statement :

`12 + "x" = (42 + "x")/2`

⇒ 2(12 + x) = 42 + x ...(by cross multiplying)

⇒ 24 + 2x = 42 + x

⇒ 2x - x = 42 - 24

⇒ x = 18

Hence after 18 years, the age of the son will be half the age of the man

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