Five years ago, A was thrice as old as B and ten years later, A shall

1.	Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What are the present ages of A and B?
Answer» Let the age of A = x years And the age of B = y years Five years ago, A’s age = (x – 5) years B’s age = (y – 5) years According to the question, (x – 5) = 3(y – 5) ⇒ x – 5 = 3y – 15 ⇒ x = 3y – 10 …(i) Ten years later, A’s age = (x + 10) B’s age = (y + 10) According to the question, (x + 10) = 2(y + 10) ⇒ x + 10 = 2y + 20 ⇒ x = 2y + 10 …(ii) From Eq. (i) and (ii), we get 3y – 10 = 2y + 10 ⇒ 3y – 2y = 10 + 10 ⇒ y = 20 On putting the value of y = 20 in Eq. (i), we get x = 3(20) – 10 ⇒ x = 50 Hence, the age of person A is 50 years and Age of B is 20 years.

Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What are the present ages of A and B?

Answer»

Let the age of A = x years

And the age of B = y years

Five years ago,

A’s age = (x – 5) years

B’s age = (y – 5) years

According to the question,

(x – 5) = 3(y – 5)

⇒ x – 5 = 3y – 15

⇒ x = 3y – 10 …(i)

Ten years later,

A’s age = (x + 10)

B’s age = (y + 10)

According to the question,

(x + 10) = 2(y + 10)

⇒ x + 10 = 2y + 20

⇒ x = 2y + 10 …(ii)

From Eq. (i) and (ii), we get

3y – 10 = 2y + 10

⇒ 3y – 2y = 10 + 10

⇒ y = 20

On putting the value of y = 20 in Eq. (i), we get

x = 3(20) – 10

⇒ x = 50

Hence, the age of person A is 50 years and Age of B is 20 years.