Five years ago, Mayank's mother was three times as old as Mayank. After five years she will be twice as old as Mayank. The present age of Mayank is :

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.