Multiple choice

Twice the son's age in years is added to the father's age, the sum is $70$. But if twice the father's age is added to the son's age, the sum is $95$. Then the ages of father and son respectively are

  1. $30$ yrs, $10$ yrs
  2. $40$ yrs, $15$ yrs
  3. $45$ yrs, $20$ yrs

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let F be father's age and S be son's age. 2S + F = 70 and 2F + S = 95. Multiply the first by 2: 4S + 2F = 140. Subtract the second: 3S = 45, so S = 15. Then F = 70 - 2(15) = 40.

AI explanation

Let the son's present age be x years and the father's present age be y years. Forming the simultaneous linear equations based on the given conditions gives 2x + y = 70 and x + 2y = 95. Multiplying the first equation by 2 gives 4x + 2y = 140, and subtracting the second equation from this result gives 3x = 45, so x = 15. Substituting 15 for x in the first equation gives 30 + y = 70, which means y = 40. The ages of the father and son are 40 years and 15 years respectively.

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