Sudha's grandfather was 8 time older to her 16 years ago. He would be 3 times of her age 8 years from now. Eight years ago, what was the ratio of Sudha's age to that of her grandfather?

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 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 the present ages of A and B are 5x and 3x years respectively. Then
A's age 4 years ago = 5x - 4
B's age 4 years hence = 3x + 4
According to question,
The ratio between A's age 4 years ago and B's age 4 years hence is 1 : 1
(5x - 4)/(3x + 4) = 1 : 1 = 1
? 5x - 4 = 3x + 4
? 2x = 8
? x = 4
present ages of A and B are 20 and 12 years.
The ratio between A's age 4 years hence and B's age 4 year ago is:
Hence, required ratio = (20 + 4) : (12 - 4) = 24 : 8 = 3: 1

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

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

Let us assume Q age is Q years , R age is R years and T age is T years.
According to question,
Q is as much younger than R as he is older than T
Age of Q - T = R - Q
? Q = (R + T)/2
If sum of the ages of R and T is 50 years.
Hence, age of Q = 50/2 = 25 years
Here, absolute value of age of R is not known.
So the difference between R and Q's age cannot be determined. Hence, data is inadequate.

Let us assume the age of youngest child be P years.
Then according to question,
The age of 5 children born after every 3 years will be P , P + 3,
P + 6, P + 9, P + 12.
Now as we know from the given question
The sum of the ages of 5 children born at the interval of 3 years each is 50 years
P + (P + 3) + (P + 6) + (P + 9) + (P + 12) = 50
? 5P + 30 = 50
? 5P = 20
? P = 4 years

Let us assume the present age of child is P years.
Then according to question,
I was as old as you are at present at the time of your birth.
Father's age were at the time of son's birth = P years
Again According to question
Present age of father = 38
Father's age were at the time of son's birth + Present age of Son = 38
P + P = 38
2P = 38
? P = 19 years
Hence, 5 years ago the age of son was 19 - 5 = 14 years