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      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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