Mathematics
5 years ago, A was thrice as old as B and 10 years later A shall be twice as old as B. What are the present ages of A and B?
Linear Equations
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Answer
Let x be the present age of A and y be the present age of B.
Given,
5 years ago, A was thrice as old as B.
⇒ x - 5 = 3(y - 5)
⇒ x - 5 = 3y - 15
⇒ x = 3y - 15 + 5
⇒ x = 3y - 10 …,,,,.(1)
Given,
10 years later, A shall be twice as old as B.
⇒ x + 10 = 2(y + 10)
⇒ x + 10 = 2y + 20
⇒ x = 2y + 20 - 10
⇒ x = 2y + 10 ………(2)
From equation (1) and (2), we get :
⇒ 3y - 10 = 2y + 10
⇒ 3y - 2y = 10 + 10
⇒ y = 20.
Substituting value of y in equation (1), we get :
⇒ x = 3y - 10
⇒ x = 3(20) - 10
⇒ x = 60 - 10 = 50.
Hence, A's present age = 50 years and B's present age = 20 years.
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