Question

Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?

Answer 1

Solution: Let us assume Jacob’s current age is x and his son’s current age is y.

Five years hence, Jacob’s age = x + 5 and his son’s age = y + 5

As per question;

x + 5 = 3(y + 5)

Or, x + 5 = 3y + 15

Or, x = 3y + 15 – 5 = 3y + 10

Five years ago, Jacob’s age = x – 5 and his son’s age = y – 5

As per question;

x – 5 = 7(y – 5)

Or, x – 5 = 7y – 35

Or, x = 7y – 35 + 5 = 7y – 30

Substituting the value of x from first equation in this equation, we get;

3y + 10 = 7y – 30

Or, 3y + 10 + 30 = 7y

Or, 7y – 3y = 40

Or, 4y = 40

Or, y = 10

Substituting the value of y in first equation, we get;

x = 3y + 10

Or, x = 3 x 10 + 10 = 40

Hence, Jacob’s age = 40 years and son’s age = 10 years