Question

    The question consists of two quantities,

    choose the correct option which represents the  correct relation between Q1 and Q2. Quantity I: The average age of a father, mother, son, and daughter is 22.5 years. Three years hence the average age of the father and mother is 34.5 years. If the ratio of the age of son and daughter is 2:1. Find the sum of the age of Son and daughter.  Quantity II: 7 years ago from the present, the ratio of the age of M and N is 6:7. Again after 5 years it is 10:11. Find the sum of teh present age of M and N .
    A Quantity I > Quantity II Correct Answer Incorrect Answer
    B Quantity I < Quantity II Correct Answer Incorrect Answer
    C Quantity I >= Quantity II Correct Answer Incorrect Answer
    D Quantity I <= Quantity II Correct Answer Incorrect Answer
    E Quantity I = Quantity II Correct Answer Incorrect Answer

    Solution

    ATQ, 

    Quantity I:

    Let the age of father , mother, daughter and son be F, M, D, and S.

    S/D = 2 or D= S/2

    The sum of the age of father , mother, daughter and son = F+M+D+S = 22.5 x 4 = 90 years

    Sum of the father and mothers age after 3 years = 34.5 x 2 = 69 years

    Sum of the father and mothers age at present = 69-6 = 63 years

    F+M = 63 years 

    S+D = 90-63 = 27 years 

    3S/2 = 27 

    S= 18 years

    D = 9 years. 

    S+D =27.

    Quantity II: 

    Let the present  age of M and N be m and n years.

    Ratio of therir age 7 years ago = 6:7

    (m-7)/(n-7) = 6/7

    7(m-7) = 6(n-7) 

    7m-6n =  7 —-----1

    (m+5)/(n+5) = 10/11

    11m-10n = -5—-----2

    Using 1 and 2 

    M = 25 years

    N = 28 years 

    M+N = 25+28 = 53 years

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