Question

Seven 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.​

Answer 1

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Let the age of swati be x

Let the age of varun be y

Seven years ago , swati's age = x - 7

Varun's age = y - 7

y - 7 = 5(x - 7)2

y - 7 = 5[x2 - 14x + 49 ]

y - 7 = 5x2 - 70x + 245

y = 5x2 - 70x + 252

After three years

Swati's age , x + 3

Varun's age , y + 3

x + 3 = 2/5[y + 3]

5x + 15 = 2y + 6

5x + 15 = 2(5x2 - 70x + 252) + 6

5x + 15 = 10x2 - 140x + 504 + 6

5x + 15 = 10x2 - 140x + 510

10x2 - 145x + 495 = 0

2x2 - 29x + 99 = 0

2x2 - 18x - 11x + 99 = 0

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

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

x = 11 / 2 , x = 9

By taking x = 9 , y = 27

Ans: Swati's age = 9 , Varun's Age = 27

Cheers!

Best of Luck!

Answer 2

Let swati age be x

Varun y

AtQ

X-7=(Y-7)^2 EQ 1

(x+3)=2/5(y+3) eq2

From eq 1 and 2 we get

Varun age= 27 and swati =9 years