The question consists of two quantities,

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