Q31 of 186 Page 4

Father's age is three times the sum of ages of his two children. After 5 years, his age will be twice the sum of ages of two children. Find the age of father.

Let the age of two children be x and y

So, the father’s present age = 3(x + y)


After five years,


Age of two children = (x + 5) + (y + 5) years


= ( x + y + 10) years


So, the age of father after five years = 3(x + y) + 5


= 3x + 3y + 5


According to the question,


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


⇒ 3x + 3y + 5 = 2x + 2y + 20


⇒ 3x – 2x + 3y – 2y = 20 – 5


⇒ x + y = 15


So, the age of two children = 15 years


And the age of father = 3(15) = 45years


Hence, the age of father is 45 years and the age of his two children is 15 years.


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