Question

7 years ago Varun's age was 5 times the age of Swati . 3 years hence swati age will be two fifth of Varun's age find their present age

Answer 1

Let the present age of Swati be x years.

Varun's age 7 years ago = 5 × (Age of Swati)2

∴ Varun's age = 5 × (x – 7)2

Present age of Varun = 5 ( x – 7)2 + 7 

3 years later:

Age of Swati = 2 5    × Age of Varun

∴ (x + 3) = 2 5 [{5 (x - 7) 2 + 7} + 2]

⇒ (x + 3) = 2 5 [5 (x - 7) 2 + 10]

⇒ 5(x + 3) = 2[5( x 2 + 49 - 14x) + 10]

⇒ 5x + 15 = 10( x 2 + 49 - 14x) + 20

⇒ 5x + 15 = 10 x 2 - 140x + 490 + 20

⇒ 10 x 2 - 145x + 495 = 0

⇒ 2 x 2 - 29x + 99 = 0

⇒ 2 x 2 - 18x - 11x + 99 = 0

⇒ 2x(x - 9) - 11(x - 9) = 0

⇒ (2x - 11)(x - 9) = 0

⇒ 2x - 11 = 0 or x - 9 = 0

⇒ x = 11 2 or x = 9

∴ x = 9  (As x cannot be 11 2 )

So, present age of Swati = 9 years

Present age of Varun = 5 (x - 7) 2 + 7 = 5(9 -7)2+ 7 = 5 × 4 + 7 = 20 + 7 = 27 .