Q32 of 186 Page 4

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?

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 50years and Age of B is 20years.


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