The ratio between the present ages of A and B is 5 : 3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1 : 1. The ratio between A's age 4 years hence and B's age 4 year ago is:

Let the present age of three persons are 4x, 7x and 9x years respectively.
Eight years ago, Ages of three person were 4x - 8, 7x - 8, 9x - 8 years.
According to question,
4x - 8 + 7x - 8 + 9x - 8 = 56
? 20x - 24 = 54
? 20x = 80
? x = 4
Hence, their present ages are
4 x 4 = 16 years,
7 x 4 = 28 years,
9 x 4 = 36 years respectively .

Let the present age of Divya and Namrata are 3x and 4x years respectively; then
According to question,
Ten years ago, Age of Divya = 3x - 10
Ten years ago, Age of Namrata = 4x - 10
Now According to question,
Ten years ago, the age of Divya was half of the age of Namrata
3x - 10 = (4x - 10)/2
? 6x - 20 = 4x - 10
? 2x =10
? x = 5
Hence, sum of their ages = 3x + 4x = 7x =7 x 5 = 35 years

Here, ratio of ages of Ram, Mohan and Anil = 4 : 5: 6
Let their present ages be 4x, 5x and 6x years respectively.
then 4x + 5x + 6x = 90
? 15x = 90
? x = 6
Hence, age of Mohan = 5 x 6 = 30 years

Let the present ages of Arun and Barun are x and x +14 years respectively; then
According to question, 7 years ago the ratio of their ages was 5 : 7
(x - 7)/(x + 14 - 7) = 5/7
? (x - 7)7 = 5(x+14 - 7)
? 7x - 49 = 5x + 35
? 2x = 84
? x = 42
Hence, age of Barun = 42 + 14 = 56 years

Lt us assume the present age of father is P and son age is Q.
According to question,
P + Q = 45.................. (1)
Five years ago, the father age = P - 5
Five years ago, the son age = Q - 5
According to question,
Five years ago, the product of their ages was four times the father's age at that time.
(P - 5) (Q - 5) = 4 (P - 5)
PQ - 5P - 5Q + 25 = 4P - 20
PQ - 5P - 5Q + 25 - 4P + 20 = 0
? PQ - 9P - 5Q + 45 = 0
? P(Q - 9) - 5(Q - 9) = 0
? (Q - 9) (P - 5) = 0
? (Q - 9) = 0 or (P - 5) = 0
? Q = 9 or P = 5
Put the vale of Q in equation (1), we will get.
if Q = 9 then P = 45 - 9 = 36 which is matched our answer.

If P = 5 then Q = 45 - 5 = 40 years which is not match our answer.

Method 2
Let the present ages of father and his son be x and (45 - x) years respectively;
then according to question,
(x - 5) (45 - x - 5) = 4 (45 - x -5)
? x - 5 = 4
? x = 9
Now, Father's age = 45 - x = 45 - 9 = 36 years

Let the present ages of the man and his wife are 4x and 3x years respectively; then
After 4 years ages of man and his wife will be 4x + 4 and 3x + 4 years.
According to question,
After 4 years, this ratio of their ages will be 9 : 7,
(4x + 4)/ (3x + 4) = 9/7
? (4x + 4)7 = 9(3x + 4)
? 28x + 28 = 27x + 36
? x = 8
Hence, their present ages are 4 x 8 = 32 years and 3 x 8 = 24 years
If t years ago they were married, then
(32 - t) /(24 - t) = 5/3
? (32 - t)3 = 5(24 - t)
? 96 -3t = 120 - 5t
? 2t = 24
? t = 12 years

Let us assume the age of B be P years then age of A will be P + 2 and age of C will be P/2 years.
Then according to question,
P + 2 + P + P/2 = 27
? P + P + P/2 = 27 - 2
? ( 2P + 2P + P)/2 = 25
? 5P = 25 x 2
&there; P = 50/5 = 10 years
Age of B will be 10 years.

Let us assume 16 years ago, the age of Sudha and her grandfather were x and 8x years respectively; then
Present age of Sudha = x + 16
Present age of her grandfather = 8x + 16
After 8 years age of sudha from now = x + 16 + 8
After 8 years age of grandfather from now = 8x + 16 + 8
now according to question,
He would be 3 times of her age 8 years from now.
3(x + 16 + 8) = 8x + 16 + 8
? 3x + 72 = 8x + 24
? 5x = 48
? x = 48/5
Eight years ago , sudha age = x + 16 - 8 = x + 8
Eight years ago , grandfather age = 8x + 16 - 8 = 8x + 8
Hence, required ratio = (x + 8) / (8x + 8 )
Put the vale of x , we will get
? required ratio = (48/5 + 8) / ( 8 x 45/5 + 8)
? required ratio = ((48 + 40)/5) / ( (8 x 45 + 40)/5)
? required ratio = (88/5) / ( 400/5)
? required ratio = 88 / 400
? required ratio = 11 : 50

Let us assume the A age is P , B age is Q and C age is R years.
Sum of the age of A and B age is P + Q years and B and C ages is Q + R Years.
According to question,
The sum of ages of A and B is 12 years more than the sum of ages of B and C
Here, (P + Q) = (Q + R) + 12
? (P + Q) - (Q + R) = 12
? P - R = 12
? P = R + 12
Hance, C is 12 years younger than A.

Let the present age of Ram be x years; then
8 years ago Ram age = x - 8
According to question,
His present age is 6/5 times his age at the time of marriage.
x =( x - 8) 6/5
? 5x = 6x - 48
? x = 48
Age of Ram at the time of his marriage = 48 - 8 = 40
According to question,
Ram's sister was 10 years younger to him at the time of his marriage
Hence, Ram's sister age at the time of his marriage = 40 - 10 = 30 years.
So Present age of Ram's Sister = 30 + 8 = 38