Question

7 years ago varun's age was 5 times the square of swati's age. 3 years hence, swati's age will be two- fifth of varun's age. Find their present ages​

Answer 1

let varun's and swati's present age be x years and y years respectively.

then, varun's age 7 years ago=x-7

swati's age 7 years ago=y-7

therefore,x-7=5(y-7)^2

x-7=5(y^2-14y+49)

x-7=5y^2-70y+245

x=5y^2-70y+252. .....(1)

varun's age 3 years later=x+3

swati's age 3 years ago=y+3

therefore,y+3=2/5(x+3)

5y+15=2(x+3)

5y+15=2x+6

5y+15=2(5y^2-70y+252)+6. from(1)

5y+9=10y^2-140y+504

10y^2-145y+495=0

2y^2-29y+99=0

2y^2-18y-11y+99=0

2y(y-9)-11(y-9)=0

(2y-11)(y-9)=0

2y-11=0 or,y-9=0

y=11/2 or,y=9

y=9. (age cannot be negative)

putting y=9 in (1),we get

x=5(9)^2-70(9)+252

x=5(81)-70(9)+252

x=405-630+252

x=27

hence, varun's present age is 27 years and swati's present age is 9 years.

Answer 2

$\Huge\orange{\boxed{\boxed{\underline{ANSWER}}}}$

Seven years ago,

Let Swats age be " x " years.

Then, seven years ago Varun's age was 5x² years.

Therefore Swati's present age = ( x + 7 ) yrs

.

Varun's present age = ( 5 x² + 7 ) years

Three years hence, then we have :

Swati's age = ( x + 7 + 3 )yrs = ( x + 10 ) years.

Varun's age = ( 5x² + 7 + 3 ) yrs = ( 5x² + 10 ) years.

It is given that, 3 years hence Swati's age will be 2/5 of Varun's age.

∴ x + 10 = 2/5 ( 5x² + 10 )

⇒ x + 10 = 2x² + 4

⇒ 2x² - x - 6 = 0      ( applying middle term splitting method )

⇒ 2x² - 4x + 3x - 6 =0

⇒ 2x ( x - 2 ) + 3 ( x - 2 )  = 0

⇒ ( 2x + 3 ) ( x - 2 ) = 0

⇒ x - 2 = 0

⇒ x = 2

Hence,

• Swati's  present age = ( x + 7 ) yrs = ( 2 + 7 ) = 9 years.

                                                                ( putting the value of x = 2)

• Varun's present age = ( 5x² + 10 ) yrs = ( 5 × 2² + 7 )

                                                                     

                                                                       =   27 years.