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    Question

    The average age of a father, mother, and daughter is 26 years. The average age of the mother and daughter is twice the age of the daughter. If the ages of the father and mother are in the ratio 4:3, respectively, then find the age of the father.

    A 25 yrs Correct Answer Incorrect Answer
    B 39 yrs Correct Answer Incorrect Answer
    C 45 yrs Correct Answer Incorrect Answer
    D 52 yrs Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    ATQ, Total age of father, mother, and daughter = 26 x 3 = 78 years. Let the age of the daughter be 's' years. So, average age of mother and daughter = 2s years. So, sum of ages of mother and daughter = 2 x 2s = 4s years. So, age of the mother = 4s - s = 3s years. So, age of the father = 3s x (4/3) = 4s years. ATQ: 4s + 3s + s = 78 Or, 8s = 78 So, s = 78 / 8 = 9.75 years. So, age of the father = 4s = 4 x 9.75 = 39 years. Therefore, the father is 39 years old.

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