Question

    2n years ago, the age of Rahul was four times that of

    his son and n years ago, the age of Rahul was thrice that of his son. If n years later, the sum of the ages of Rahul and his son will be 80 years, then the difference in the ages of Rahul and his son is –
    A 20 years Correct Answer Incorrect Answer
    B 30 years Correct Answer Incorrect Answer
    C 40 years Correct Answer Incorrect Answer
    D 34 years Correct Answer Incorrect Answer
    E 24 years Correct Answer Incorrect Answer

    Solution

    Let the present ages of Rahul and his son be x and y respectively. 2n years ago, => x – 2n = 4(y – 2n) => x = 4y – 6n ------ (i) n years ago, => x - n = 3(y – n) => x = 3y – 2n ------ (ii) Solving (i) and (ii) we get, => y = 4n => x = 4 × 4n – 6n = 10n Now n years later, => x + n + y + n = 80 => 4n + n + 10n + n = 80 => 16n = 80 => n = 5 Required difference = 10n – 4n = 6n = 30 years

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