A man is 3 years older than his wife and four times as old as his son. If the son becomes 15 years old after 3 years, then what is the present age of the wife?

Suppose the present age of B = P years
The present age of A - The present age of B = 2 years.
Therefore, the present age of A = P + 2 years
According to question,
Two years ago , 2( the present age of B - 2 years ) = the present age of A - 2 years
2 (P ? 2) = P + 2 ? 2
? 2P ? 4 = P
? 2P ? P = 4
? P = 4
Age of B = 4 years
Age of A = P + 2 = 4 + 2 = 6 years

Sum of ages of mother, daughter and son (i.e., 3 persons) = 87 years.
After 8 years , Sum of their ages = Sum of ages of mother, daughter and son + ( 8 x 3 ) = 87 + (8 × 3) = 87 + 24 = 111 years

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.

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 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

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