Q. 423.9( 25 Votes )

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.

Answer :

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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