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.