Correct Answer - Option 4 : 20, 2
Given∶
Chinki’s age = five times the square of Minki’s age
10 years later, Chinki’s age = 6 years more than twice the age of Minki.
Formula Used∶
Concept of Quadratic Equations, Factorization (Splitting the middle term method)
Calculation∶
Let the present age of Minki’s be ‘x’ years
Then, the present age of Chinki is (5x2) years
After 10 years, Minki’s age = (x + 10) years
Chinki’s age = (5x2 + 10) years
According to question,
5x2 + 10 = 2(x + 10) + 6
⇒ 5x2 + 10 = 2x + 20 + 6
⇒ 5x2- 2x – 16 = 0
⇒ 5x2- 10x + 8x – 16 = 0
⇒ 5x(x – 2) + 8(x – 2) = 0
⇒ (x – 2) (5x + 8) = 0
⇒ x – 2 = 0 or 5x + 8 = 0
x = 2 or x = -8/5
x can’t be -8/5, as age can not be negative.
So, Minki’s age = x = 2 years.
And Chinki’s age = 5x2 = 5 × (2)2 = 5 × 4 = 20 years
∴ Chinki’s present age is 20 years and Minki’s present age is 2 years.