# Five years hence, a man's age will be three times the age of his son. Five years ago, the man was seven times as old as his son. Find their present ages.

Let the age of the man and his son be x and y years respectively.

According to question -

Five years hence, a man's age will be three times the age of his son

x + 5 = 3(y + 5)

⇒ x - 3y = 10.....(1)

and,

Five years ago, the man was seven times as old as his son

x - 5 = 7(y - 5)

⇒ x - 7y = - 30.....(2)

Subtracting Equation (2) from (1), we get -

⇒ -3y + 7y = 10 + 30
⇒ 4y = 40
⇒ y = 10

Substituting the value of y in equation (1), we get -

⇒ x - 3(10) = 10
⇒ x = 30 + 10
⇒ x = 40

Thus, Man's age, x = 40 years
and son's age, y = 10 years

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