Question

Nine times the age of Chantu exceeds four times the age of Bantu by 1 and six times the square of the age of Bantu exceeds twenty-nine times the square of the age of Chantu by 1. Find the present ages of Chantu and Bantu.
1. 5, 11 years
2. 6, 12 years 
3. 7, 14 years 
4. 2, 10 years 

Answer 1

Correct Answer - Option 1 : 5, 11 years

Given∶

9 times Chantu’s age = 4 times Bantu’s age + 1

6 times the square of Bantu’s age = 29 times the square of Chantu’s age + 1

Formula Used∶

Concept of Quadratic Equations, Factorization (Splitting the middle term method)

Calculation∶

Let the age of Chantu’s be ‘x’ years and age of Bantu’s age be ‘y’ years.

According to the question,

9x = 4y + 1

⇒ y = (9x – 1)/4     ----(1)

Also, 6y² = 29x² + 1     ----(2)

put y = (9x – 1)/4 in eq. (2)

6 [(9x – 1)/4]² = 29x² + 1

⇒ 6 (81x² – 18x + 1)/16 = 29x² + 1

⇒ 243x² – 54x + 3 = 232x² + 8

⇒ 11x² – 54x – 5 = 0

⇒ 11x² – 55x + x – 5 = 0

⇒ (x – 5)(11x + 1) = 0

x = 5 or x = -1/11,

x = -1/11, which can’t be possible as age cannot be negative.

So, put x = 5 in eq. (1)

Y = (9x- 1)/4 = (9 × 5 – 1) = 44/4 = 11

∴ Chantu’s age is 5 years and Bantu’s age is 11 years.