7 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.
Answers
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]
⇒ 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
Answer:
Step-by-step explanation:
Let seven years, age of Swati was x years and age of Varun was 5x² years
Present age of Swati = ( x + 7 ) years
Present age of Varun = ( 5x² + 7 ) years
Given, after 3 years swati's age will be 2 / 5 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 = age of varun after 3 years
( x + 10 ) = 2 / 5 × ( 5x² + 10 )
( 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,
present age of Swati = ( 2 + 7 ) = 9 years
present age of Varun = 5(2)²+7=27 years
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