Let us assume 16 years ago, the age of Sudha and her grandfather were x and 8x years respectively.

Correct Option: A

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.

Correct Option: B

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.

Method 1
Let us assume the present age of Mayank is X and his mother age is Y.
Five years ago, Mayank's age = X - 5
Five years ago, Mayank's mother age = Y - 5

After five years, Mayank's age = X + 5
After five years , Mayank's mother age = Y + 5


Method 2
Let us assume the present age of Mayank be P, then the 5 years before Mayank's age = P - 5
According to Question
Age of his mother before 5 years = 3 x (P - 5 )
Present age of his mother = 3 x (P - 5 ) + 5
After 5 Years Mayank's age = P + 5
After 5 Years Mother' age = 3 x (P - 5 ) + 5 + 5

Correct Option: B

Method (1)
Let us assume the present age of Mayank is X and his mother age is Y.
Five years ago, Mayank's age = X - 5
Five years ago, Mayank's mother age = Y - 5
According to question,
Five years ago, Mayank's mother was three times as old as Mayank.
Y - 5 = 3 (X - 5)
⇒ Y - 5 = 3X - 15
⇒ 3X - Y = 15 - 5
⇒ 3X - Y = 10................(1)
Again According to question,
After five years, Mayank's age = X + 5
After five years , Mayank's mother age = Y + 5
After five years she will be twice as old as Mayank.
Y + 5 = 2 ( X + 5 )
⇒ Y + 5 = 2X + 10
⇒ Y - 2X = 10 - 5
⇒ Y - 2X = 5 ....................(2)
Add the equation (1) and (2), we will get
3X - Y + Y - 2X = 10 + 5
X = 15
Put the vale of X in equation (2), We will get
Y - 2 x 15 = 5
Y + 30 + 5 = 35 years
Mayank' Present Age is 15 years and mother age is 35 year.

Method 2
Let us assume the present age of Mayank be P, then the 5 years before Mayank's age = P - 5
According to Question
Age of his mother before 5 years = 3 x (P - 5 )
Present age of his mother = 3 x (P - 5 ) + 5
After 5 Years Mayank's age = P + 5
After 5 Years Mother' age = 3 x (P - 5 ) + 5 + 5
Now again according to question,
After five years she will be twice as old as Mayank, then
3 x (P - 5 ) + 5 + 5 = 2 (P + 5)
⇒ 3P - 5 = 2P + 10
⇒ 3P - 2P = 10 + 5
⇒ P = 15
Mayank's present Age is 15 years.

Let us assume Q age is Q years , R age is R years and T age is T years.

Correct Option: D

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.

Correct Option: C

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