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
Suppose age of son = P years
Age of the man = 4P years
Age of man's wife = 4P ? 3 years
According to the question,
After 3 years, age of son + 3 years = 15
P + 3 = 15
? P = 15 ? 3 = 12 years
Now, age of wife = 4P ? 3 years
age of wife = 4 × 12 ? 3 years
age of wife = 48 ? 3 years
age of wife = 45 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.
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