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    Question

    The average of the present ages of A, B, C and

    D is (y-3) years. 12 years hence, the ratio between the ages of A and C is 9:8 respectively. The age of B is 6 years younger than D. The value of ‘y’ is the multiple of 12 but it should be less than 60. If the present age of  D is 54 years, then which of the following is/are the possible values of ‘y’? (i) 12 (ii) 24 (iii) 36 (iv) 48
    A only (ii) Correct Answer Incorrect Answer
    B only (ii) and (iii) Correct Answer Incorrect Answer
    C only (iv) Correct Answer Incorrect Answer
    D only (i) and (iv) Correct Answer Incorrect Answer
    E only (i) and (iii) Correct Answer Incorrect Answer

    Solution

    If the present age of  D is 54 years.

    The age of B is 6 years younger than D.

    present age of B = 54-6 = 48 years

    The average of the present ages of A, B, C and D is (y-3) years.

    Sum of the present ages of A, B, C and D = 4(y-3)

    present age of A + present age of B + present age of C + present age of D = 4(y-3)

    present age of A+48+present age of C+54 = 4(y-3)

    12 years hence, the ratio between the ages of A and C is 9:8 respectively.

    Let’s assume 12 years hence, the ages of A and C are ‘9a‘ and ‘8a‘ respectively.

    (9a-12)+48+(8a-12)+54 = 4(y-3)    Eq.(i)

    (i) 12

    Put the possible value of ‘y’ in Eq.(i).

    (9a-12)+48+(8a-12)+54 = 4x(12-3)

    (9a-12)+48+(8a-12)+54 = 4x9

    17a+78 = 36

    Here the value of ‘a’ will be negative. So this is not the possible value of ‘y’.

    (ii) 24

    Put the possible value of ‘y’ in Eq.(i).

    (9a-12)+48+(8a-12)+54 = 4x(24-3)

    17a+78 = 4x21

    17a = 84-78 = 6

    Here the value of ‘a’ will be in fractions. So this is not the possible value of ‘y’.

    (iii) 36

    Put the possible value of ‘y’ in Eq.(i).

    (9a-12)+48+(8a-12)+54 = 4x(36-3)

    17a+78 = 4x33

    17a+78 = 132

    17a = 132-78

    17a = 54

    Here the value of ‘a’ will be in fractions. So this is not the possible value of ‘y’.

    (iv) 48

    Put the possible value of ‘y’ in Eq.(i).

    (9a-12)+48+(8a-12)+54 = 4x(48-3)

    17a+78 = 4x45

    17a+78 = 180

    17a = 180-78

    17a = 102

    a = 6

    Here the value of ‘a’ is a natural number. So this is the only possible value of ‘y’.

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