Question

Seven years ago Raghav's age was five times the Square of Namita's age, After three years from now Namita's age will be 2/5 times of Raghav's age. Find the difference between tge ages of Raghav and Namita .

Answer 1

hey bro .....Eshansingh......☺
_____________________
.here is ur answer. .
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♠let the Namita's 's age 7 years ago be x years..

♣then ,the Raghav"s Age 7year ago =5x^2.

but,now

Namita's present age (x+7)

Raghav"s present age =(5x^2+7)years

and again ,

Namita's age 3 year hence =(x+7+3)year
=(x+10)years

Raghav 's age 3yesr hence =5x^2+7+3

=5x^2+10

since ,x+10=2/5(5x^2+10)
♦
=>5x+50=10x^2+20
=>10x^2-5x-30=0
=>
=>2x^2-x-6 =0
=>2x^2-4x-3x-6=0
=>2x(x-2)+3(x-2)=0
=>(x-2)(2x+3)=0
=>x=2 and x=-3/2......

♠【since ,age can't be negative hence x=-3/2neglected 】

now,remaining is x=2 ...

so,Namita" s present age =(2+7)year =9years. .

and ,Raghav 's present age =(5×2^2+7)years.

=27 years. ......

hope it help you ....☺☺☺☺☺

@Rajukumar☺☺☺

Answer 2

Let the present age of Namita = x years.

Seven Years ago The Age of Namita = (x - 7) years.

Then the age of Raghav = 5(x - 7)^2

Therefore Raghav's present age = 5(x - 7)^2 + 7

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

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

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




Three Years Hence:

The age of Namita = (x + 3) years.

The age of Raghav = (5x^2 - 70x + 252) + 3

                                 = 5x^2 - 70x + 255 years.   




Given that Namita's age will be 2/5 times of Raghav's age.

x + 3 = 2/5(5x^2 - 70x + 255) 

5x + 15 = 10x^2 - 140x + 510

10x^2 - 140x + 510 - 15 = 5x + 15

10x^2 - 140x + 495 = 5x + 15

10x^2 - 145x +  495 = 0

 2x^2 - 29x + 99 = 0

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

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

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

2x = 11 (or) x = 9

x = 11/2 (or) x = 9.

Since age cannot be a fraction, So x = 9.

Substitute x = 9 in (1), we get

5x^2 - 70x + 252

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

405 - 630 + 252

657 - 630

= 27 years.



Therefore the present age of Namita = 9 years.

 Therefore the present age of Raghav = 27 years.


The difference between their ages = 18 years.



Hope this helps!