Question

Hello friends,

Solve this.

7 years ago Varun's age was five times the square of Swati's Age. 3 years hence, Swati age will be two-fifth of Varun age. Find their present ages.

Answer 1

Hey there !!

→ Let Swati's age 7 years ago be x years.

→ Then, Varun's age 7 years ago = 5x² years.

→ Swati's present age = ( x + 7 ) years.

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

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

▶Now,

A/Q,


$\bf \therefore (x + 10) = \frac{2}{5} (5 {x}^{2} + 10).$


=> 5x + 50 = 10x² + 20.

=> 10x² - 5x = 50 - 20.

=> 10x² - 5x = 30.

=> 10x² - 5x - 30 = 0.

=> 5( 2x² - x - 6 ) = 0.

=> 2x² - x - 6 = 0.

=> 2x² - 4x + 3x - 6 = 0.

=> 2x( x - 2 ) + 3( x - 2) = 0.

=> ( x - 2 ) ( 2x + 3 ) = 0.

=> x - 2 = 0. |. 2x + 3 = 0.

=> x = 2. | x = $\frac{ - 3 }{2} .$


$\huge \boxed{ \boxed{ \bf => x = 2. }}$


[ => Age cannot be negative ].

↪ Swati's present age = ( x + 7 ) years.

= ( 2 + 7 ) years


$\huge \boxed{ = 9 \: years . }$


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

= ( 5 × 2² + 7 ) years.


$\huge \boxed{ = 27 \: years . }$


✔✔ Hence, it is solved ✅✅.

____________________________________


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$\huge \bf{ \# \mathcal{B}e \mathcal{B}rainly.}$

Answer 2

Answer :-

_____________________

Given ,

• 7 years ago Varun's age was five times the square of Swati's Age. And 3 years hence, Swati age will be two-fifth of Varun age.

To find ,

( i ) The present age of Swati.

( ii ) The present age of Varun.

Now let ,

7 years ago the age of Swati was x

So according to question ,

7 years ago the age of Varun was 5x²

So , the present age of Swati is ( x + 7 )

And , the present age of Varun is ( 5x² + 7 )

And , 3 years hence ,

The age of Swati will be ( x + 7 + 3 ) = ( x + 10 )

And the age of Varun will be ( 5x² + 7 + 3 ) = ( 5x² + 10 )

Now ,

According to the question ,

2 / 5 ( 5x² + 10 ) = ( x + 10 )

[ °•° 3 years hence, Swati age will be two-fifth of Varun age. Find their present ages. ]

=> 2 ( 5x² + 10 ) = 5 ( x + 10 )

=> 10x² + 20 = 5x + 50

=> 10x² - 5x + 20 - 50 = 0

=> 10x² - 5x - 30 = 0

=> 5 ( 2x² - x - 6 ) = 0

=> 2x² - ( 4 - 3 )x - 6 = 0

=> 2x² - 4x + 3x - 6 = 0

=> 2x ( x - 2 ) + 3 ( x - 2 ) = 0

=> ( x - 2 ) + ( 2x + 3 ) = 0

Now ,

Either ,

( x - 2 ) = 0

x = 2

Or ,

( 2x + 3 ) = 0

2x = - 3

x = - 3 / 2 [ • But it's not possible cause age never be negative ]

So , x = 2

Now ,

•°• The present age of Swati is ( x + 7 )

= 2 + 7

= 9 [ ★ Required answer ( i ) ]

•°• The present age of Varun is ( 5x² + 7 )

= 5 × ( 2 )² + 7

= 5 × 4 + 7

= 20 + 7

= 27 [ ★ Required answer ( ii ) ]

__________________________

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