Question

Chinki and Minki are two sisters. Chinki’s age is five times the square of the age of her sister Minki. Ten years hence, the age of Chinki will be 6 years more than twice the age of Minki. Find the present age of Chinki and Minki.
1. 30, 3
2. 30, 2
3. 20, 3
4. 20, 2

Answer 1

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.