Question

At present Asha's age is 2 years more than the square of her daughter Nisha's age.When Nisha grows to her mother's present age ,Asha's age would be one year less than 10 times the present age of Nisha.Find the present ages of both Asha and Nisha.

Answer 1

Solution:-

Let Nisha's present age be 'x' years
So, Asha's present age will be = x² + 2
Difference between Nisha'a age and Asha's age = x² + 2 - x
Now, it is given that when grows to her mother's age i.e. after x² + 2 - x years
... Nisha will grow to Asha's age.
To calculate Asha's age, when Nisha's age will be x² + 2 years, we will add 
x² + 2 to x² + 2 - x
i.e. x² + 2 + x² + 2 - x = 10x - 1
⇒ 2x² + 4 + 1 - x - 10x = 0
⇒ 2x² - 11x + 5 = 0
⇒ 2x² - 10x - x + 5 = 0
⇒ 2x(x - 5) - 1(x - 5) = 0
⇒ (2x - 1) (x - 5) = 0
⇒ 2x = 1 
⇒ x = 1/2, which is not possible.
So, x = 5 is correct value.
So, Nisha's present age is 5 years 
Asha's age = 5² + 2 
= 27 years
Answer.

Answer 2

Answer:

Let, Nisha’s present age be = x year

Therefore, according to the first condition, Asha's present age = x2 + 2

Nisha grows to her mother's present age after [(x² + 2) – x] years.

Then, Asha's age will become (x² + 2) + [(x² + 2) –x] years.

• According to the question :

⟹ (x² + 2) + [(x² + 2) – x] = 10x – 1

⟹ 2x² – x + 4 = 10x – 1

⟹ 2x² – 11x + 5 = 0

⟹ 2x² – 10x – x + 5= 0

⟹ 2x (x – 5) –1(x – 5) = 0

⟹ (x – 5) (2x – 1) = 0

⟹ (x – 5) = 0 or (2x – 1) = 0

⟹ x = 5 or 1/2

Ignoring x = 1/2 because then Asha’s age = x² + 2 = which is not possible.

Hence, Present Age of Nisha = 5 years

And Present Age of Asha = x² + 2 = (5)² + 2 = 25 + 2 = 27 years