Question

Four years ago, age of a person was 9 times that of his son. Four years later, the
age of the person will be 4 years less than four times the age of his son at that time.
Write the equatioirfor the statement.​

Answer 1

Given :-

▪ Four years ago, Age of a person was 9 times that of his son. Four years later, The age of the person will be 4 years less than four times the age of his son.

To Find :-

▪ Equation for the statement.

▪ Present ages of the father and his son.

Solution :-

Let the present ages of father and his son be x and y respectively.

According to the Question,

4 years ago :

⇒ Age of father = 9 ( Son's age )

⇒ (x - 4) = 9 × (y - 4)

⇒ x - 4 = 9y - 36

⇒ x - 9y = -32 ...(1)

Also,

4 years later :

⇒ Age of father = 4 ( Son's age ) - 4

⇒ (x + 4) = 4(y + 4) - 4

⇒ x + 4 = 4y + 16 - 4

⇒ x - 4y = 16 - 8

⇒ x - 4y = 8 ...(2)

Hence, The equations for the given condition are

• x - 9y = -32
• x - 4y = 8

Let's find their present ages,

Subtract (2) from (1)

⇒ x - 9y - (x - 4y) = -32 - 8

⇒ x - 9y - x + 4y = -40

⇒ -5y = -40

⇒ y = 8

Substituting [y = 8] in (2)

⇒ x - 4×8 = 8

⇒ x - 32 = 8

⇒ x = 40

Hence, The present ages of the father and his son are :-

• Father's age : 40 years
• Son's age : 8 years