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 .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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