Q. 414.6( 20 Votes )

# Seven years ago Varun's age was five times the square of Swati's age. Three years hence, Swati's age will be two–fifth of Varun's age. Find their present ages.

Let seven years, age of Swati was x years and age of Varun was years.

Present age of Swati = (x + 7) years

Present age of Varun = (5x2 + 7) years

Given, after 3 years swati's age will be th of Varun's age.

Age of Swati after 3 years = (x + 7 + 3) years = (x + 10) years

Age of Varun after 3 years = (5x2 + 7 + 3) years = (5x2 + 10) years

Given, age of Swati after 3 years = Two–fifths age of varun after 3 years

(x + 10) = 2(x2 + 2)

x + 10 = 2x2 + 4

2x2 – x + 4 – 10 = 0

2x2 – x – 6 = 0

2x2 – 4x + 3x – 6 = 0

2x(x – 2) + 3(x – 2) = 0

x = 2 [ Age can't be negative ]

Therefore, the present age of Swati = (2 + 7) = 9 year and the present age of Varun = 5(2)2+7=27 years.

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