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If twice the son’s age in years is added to the father’s age; the sum is 70 years. But, if twice the father’s age is added to the son’s age, the sum is 95 years. Find the ages of father and the son.

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An important and exam oriented question from linear equations in two variables in which we have to find the age of father and son if twice the son’s age in years is added to the father’s age; the sum is 70 years. But, if twice the father’s age is added to the son’s age, the sum is 95 years.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 44

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  1. Currently,  if father’s age is x and son’s age is y,

    then given, x+2y=70 — (1)

    2x+y=95 — (2)

    Multiplying equation  (1) with 2 we get, 2x+4y=140 — (3)

    Subtracting equation (2) from (3), we get 3y=45y=15

     

    Substituting y=15 in the equation (2), we get

    2x+15=95x=40

    Hence, the father is 40 years old and the son is 15 years old.

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