Let the present age of Divya and Namrata are 3x and 4x years respectively;

Correct Option: A

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 the present age of three persons are 4x, 7x and 9x years respectively.

Correct Option: C

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 ages of A and B are 5x and 3x years respectively.

Correct Option: B

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 ages of the man and his wife are 4x and 3x years respectively.

Correct Option: B

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.

Correct Option: A

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.