Question

present Mahesh's age (in years) is 2 more than the square of his son Varun's age. When Varun grows to his father's present age, Mahesh's age would be one year less than 10 times the present age of Varun. Using the above information answer the following questions. (1) Mahesh's present age is [1] (1) 25 years (3) 29 years (ii) Varun's age after (1) 5 years (3) 9 years (2) 27 years (4) 31 years (2) 7 years (4) 11 years (i) Difference between the present ages of Mahesh and Varun is​

Answer 1

Answer:

Let Varun’s present age be x

So, according to the provided information,

Mahesh’s age = x^2 + 2

⇒ x = x^2 + 2

⇒ x^2 - x + 2 = 0 -------------------- (i)

Also given that,

10x - 1 = (x^2 + 2)

⇒ 10 - 1 - (x^2 +2) = 0 ----------------- (ii)

From equation (i) & (ii),

$tex] {x}^{2} + 2 - x = 10 - 1 - ( {x}^{2} + 2) \\ ⇒2 {x}^{2} - 11x + 5 = 0 \\ ⇒2 {x}^{2} - x - 10x + 5 = 0 \\ x(2x - 1) - 5(2x - 1) = 0 \\ ⇒(x - 5)(2x - 1) = 0 \\ ⇒x = 5 \: or \: x = \frac{1}{2}$

[/tex]

x = 5 [since age cannot be in fraction]

So, Varun’s present age = 5

Mahesh’s present age = 27

i》 2) 27 years

ii》 3) 9 years

iii》3) 22 years

iv》2) 32 years

Answer 2

Step-by-step explanation:

Answer:

Let Varun’s present age be x

So, according to the provided information,

Mahesh’s age = x^2 + 2

⇒ x = x^2 + 2

⇒ x^2 - x + 2 = 0 -------------------- (i)

Also given that,

10x - 1 = (x^2 + 2)

⇒ 10 - 1 - (x^2 +2) = 0 ----------------- (ii)

From equation (i) & (ii),

\begin{gathered}tex] {x}^{2} + 2 - x = 10 - 1 - ( {x}^{2} + 2) \\ ⇒2 {x}^{2} - 11x + 5 = 0 \\ ⇒2 {x}^{2} - x - 10x + 5 = 0 \\ x(2x - 1) - 5(2x - 1) = 0 \\ ⇒(x - 5)(2x - 1) = 0 \\ ⇒x = 5 \: or \: x = \frac{1}{2} \end{gathered}

tex]x

2

+2−x=10−1−(x

2

+2)

⇒2x

2

−11x+5=0

⇒2x

2

−x−10x+5=0

x(2x−1)−5(2x−1)=0

⇒(x−5)(2x−1)=0

⇒x=5orx=

2

1

[/tex]

x = 5 [since age cannot be in fraction]

So, Varun’s present age = 5

Mahesh’s present age = 27

i》 2) 27 years

ii》 3) 9 years

iii》3) 22 years

iv》2) 32 years