Question

Ten years later, A will be twice as old as B and five years ago, A was three times as old as B. What are the present ages of A and B.

Answer 1

Let the present ages of A be x years and that of B be y years 

From the question it’s given that, 

After 10 years, A’s age will be (x +10) years and B’s age will be (y + 10) years. 

Furthermore, the relation between their ages after 10 years is given below 

x + 10 = 2(y + 10) 

⇒ x + 10 = 2y + 20 

⇒ x – 2y - 10 = 0…….. (i) 

Also again from the question it’s given as, 

Before 5 years, the age of A was (x – 5) years and the age of B was (y – 5) years. 

So, the equation formed is 

x – 5 = 3(y - 5)

⇒ x – 5 = 3y – 15

⇒ x – 3y + 10 = 0…….. (ii)

Thus, by solving (i) and (ii), we get the required solution

Using cross-multiplication, we get,

⇒ x = 50, y = 20

Hence, the present age of A is 50 years and the present age if B is 20 years.