prince00113 wrote:

a family has only one son. The father says "After 'x' years, my age will be six times the age of my son". The mother says, "After X years, my age will be 4 times the age of my son". What will be the combined age (integer value) of the thee-member family after 'x' years ?

1. the age difference between the parents is 16 years.

2. After 'x' years the son will be twice as old as he is now

F, M, S=Father's, Mother's & Son's initial age.

F + x = 6(S + x) .... (I)

M + x = 4(S + x) .... (II)

We need to find the value of

F + M + S + 3x 1) |F-M| = 16

Now, if we subtract the equations, (I) - (II), we get

F - M = 2(S + x)

or S + x = 8 .... (III)

Now, if we add the equations, (I) + (II), we get

F + M + 2x = 10S + 10x

Adding S + x on both sides,

F + M + S + 3x = 10S + 10x + S + x ....

(This is what is what our initial equation looks like, we can now put in the value of S + x = 8 from (III) to get the value)Thus, F + M + S + 3x = 80 + 8 = 88.

(1) is sufficient.2) S + x = 2S or x = 2S - S

which means that x = S.

F + x = 6 (2S) or F + S= 12S or F = 11S

M + x = 4(2S) or M + S= 8S or M = 7S

Since no relation is mentioned between F & M, we cant find the required value.

(2) is insufficientAnswer is (A)