Question

Ram’s age was three times as old as his son two years age. Two years hence, twice of his age will be equal to five times that of his son . Find their present age .

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Answer 1

GIVEN :

† Ram’s age was three times as old as his son two years age.

† Two years hence, twice of his age will be equal to five times that of his son .

TO FIND :

† Find their present age .

SOLUTION :

Let ,

Present Age of Ram be x yrs

Present Age of Son be y yrs.

★ 2 YEARS AGO (Past):

↦ Ram = Present - 2 = (x - 2) yrs

↦ Son = Present - 2 = (y-2) yrs

‡ According to the Question :

✧ Ram Three times of Son

⇥ (x - 2) = 3 ×(y-2)

⇥ x - 2 = 3y - 6

⇥ x = 3y - 6+2

⇥ x = 3y - 4 -- eq.( 1 )

★ 2 YEARS HENCE (Future):

↦ Ram = Present + 2 = (x + 2) yrs

↦ Son = Present + 2 = (y + 2) yrs

‡ According to the Question Now :

✧ Twice of Father = Five times of Son

⇥ 2 x (x + 2) = 5 x (y + 2)

Putting the value of x from eq.(1)

⇥2 × (3 y - 4 + 2) = 5 × (y + 2)

⇥2x (3y - 2) = 5 × (y + 2)

⇥ 6 y - 4 = 5 y + 10

⇥ 6 y - 5 y = 10 + 4

⇥ y = 14 yrs

Putting value of y in eq.(1)

↦x = 3 y - 4

↦ x = 3(14) - 4

↦ x = 42 - 4

↦ x = 38 yrs

PRESENT AGES:

▸ Ram = x = 38 Years

▸ Son = y = 14 Years

∴ Present Age of Father and Son will be 38 Years and 14 Years respectively.