A man’s age is three times the sum of the ages of his two sons. Afte

1.	A man’s age is three times the sum of the ages of his two sons. After 5 years, his age will be twice the sum of the ages of his two sons. Find the age of the man.
Answer» Let one son is x years old and other son is y years old, Given that man’s age is 3 times the sum of ages of his two sons. Therefore, the man’s age = 3(x + y). ... (1) After 5 years the man’s age is 3(x + y) + 5. But given that after 5 years, the man’s age will be twice of the ages of his two sons. After 5 years the age of first son is x + 5 and the age of second son is y + 5. Therefore, 3(x + y) + 5 = 2((x+5) + (y+5)) ⇒ 3(x + y) + 5 = 2(x + y + 10) = 2(x + y) +20 ⇒ x + y = 20 – 5 = 15. ⇒ x + y = 15. Therefore, the man’s age = 3 (x + y) = 3 × 15 = 45 years. [From equation (1)]

A man’s age is three times the sum of the ages of his two sons. After 5 years, his age will be twice the sum of the ages of his two sons. Find the age of the man.

Answer»

Let one son is x years old and other son is y years old,

Given that man’s age is 3 times the sum of ages of his two sons.

Therefore, the man’s age = 3(x + y). ... (1)

After 5 years the man’s age is 3(x + y) + 5.

But given that after 5 years, the man’s age will be twice of the ages of his two sons. After 5 years the age of first son is x + 5 and the age of second son is y + 5.

Therefore, 3(x + y) + 5 = 2((x+5) + (y+5))

⇒ 3(x + y) + 5 = 2(x + y + 10) = 2(x + y) +20

⇒ x + y = 20 – 5 = 15.

⇒ x + y = 15.

Therefore, the man’s age = 3 (x + y) = 3 × 15 = 45 years. [From equation (1)]

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