Q41 of 168 Page 7

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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