MathematicsSeven years ago, Varun’s age was five times the square of Swati’s age. Three years hence, Swati’s age will be two-fifths of Varun’s age. Find their present ages.

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


  1. A
    Swati and Varun's present ages are 9 years and 27 years respectively.
  2. B
     Swati and Varun’s present ages are 8 years and 27 years respectively.
  3. C
    Swati and Varun's present ages are 9 years and 45 years respectively.
  4. D
    Swati and Varun's present ages are 9 years and 18 years respectively. 

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    Solution:

    Given Varun's age was five times the square of Swati's age. And after 3 years,  Swati's age will be two-fifth of Varun's age.
    Let seven years ago, Swati's age was x years and Varun’s age was 5x2 years. Then, Swati's present age = (x + 7) years Varun's present age= (5x2 + 7)  years
    Three years hence,
    Swati's age = (x + 7 +3)
    ⇒ Swati's age = x + 10 years
    Varun's age = (5x2 + 7+ 3)
    ⇒Varun's age = (5x2 +10​) years
    According to question,
    x + 10=25(5x2+10​)
    ⇒x + 10=(2x2+4​)
    ⇒2x2-x-6=0
    ⇒2x2-4x+3x-6=0
    ⇒2x+3x-2=0
    Now,
    x-2=0
    ⇒x=2
    Also,
    2x+3=0
    ⇒x=-32 This is not possible, because age is always positive. So x=2.
    Hence Swati's present age = 2+7years ⇒ Swati’s age = 9 years
    Varun's present age = (5x2 + 7) years ⇒Varun's age =(522 + 7)
    ⇒Varun's age =5×4+7
    ⇒Varun's age = 27 years
    Therefore, Swati and Varun's present ages are 9 years and 27 years respectively.
    Hence, the required option is 1.
     
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