Mathematics
The age of a man is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children at that time. Find the present age of the man.
Linear Equations
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Answer
Let present age of man be x years and sum of the ages of his two children be y years.
Given,
The age of a man is twice the sum of the ages of his two children.
∴ x = 2y ……..(1)
Given,
After 20 years, his age will be equal to the sum of the ages of his children at that time.
After 20 years,
Age of man = (x + 20) years
Sum of ages of his children = (y + 40), as each child's age will increase by 20 years.
⇒ x + 20 = y + 40
⇒ 2y + 20 = y + 40 ………[From (1)]
⇒ 2y - y = 40 - 20
⇒ y = 20.
⇒ x = 2y = 2(20) = 40.
Hence, present age of man = 40 years.
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