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Mathematics

Five years ago, Bharat was thrice as old as Rajat. Ten years later, Bharat will be twice as old as Rajat. The difference between their present ages is :

  1. 10 years

  2. 20 years

  3. 30 years

  4. 35 years

Linear Equations

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Answer

Let x be Bharat's present age and y be Rajat's present age,

Given,

Five years ago, Bharat was thrice as old as Rajat.

⇒ x - 5 = 3(y - 5)

⇒ x - 5 = 3y - 15

⇒ x = 3y - 15 + 5

⇒ x = 3y - 10     ….(1)

Given,

Ten years later, Bharat will be twice as old as Rajat,

⇒ x + 10 = 2(y + 10)

⇒ x + 10 = 2y + 20

⇒ x = 2y + 20 - 10

⇒ x = 2y + 10     ….(2)

Substituting value of x from equation (1) in x = 2y + 10, we get :

⇒ 3y - 10 = 2y + 10

⇒ 3y - 2y = 10 + 10

⇒ y = 20 years.

Substituting value of y in equation (1), we get :

⇒ x = 3y - 10

⇒ x = 3(20) - 10

⇒ x = 60 - 10

⇒ x = 50 years.

The difference between their present ages = x - y = 50 - 20 = 30 years.

Hence, option 3 is the correct option.

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