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Six years hence a man’s age will be three times the age of his son and three years ago he was nine times as old as his son. Find their present ages.

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Let the present age of man be ‘a’ and present age of son be b.

Given,

Six years hence a man’s age will be three times the age of his son and three years ago he was nine times as old as his son

⇒ a + 6 = 3(b + 6)

⇒ a = 3b + 12 ------ (1)

Also,

Three years ago he was nine times as old as his son

⇒ a – 3 = 9(b – 3)

⇒ a = 9b – 24 ----- (2)

Equating eq1 and eq2

⇒ 3b + 12 = 9b – 24

⇒ b = 6

Thus,

a = 3b + 12 = 30

Hence age of man is 30 yrs and age of son is 6 yrs.

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