Question

6. At present Asha’s age (in years) is 2 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

SoluTioп :-

Let Nisha's age be x

Aisha's age = (x² + 2)

A/Q to question , when Nisha grows to her mother present age, means Nisha's grows = Aisha's present age - Nisha's present age = x² + 2 - x

Then, this time Aisha's age = Aisha's present age + growing time = x² + 2 + x² + 2 - x = 2x² - x + 4

Now, question said , Aisha's age = 10× times of Nisha's age -1

2x² - x + 4 = 10x -1

2x² - 11x + 5 = 0

2x² -10x - x + 5 = 0

x = 5 and 1/2 x ≠ 1/2 because age doesn't in moths

Hence , Nisha's present age = 5 years

Aisha's present age = (5)² + 2 = 27 years

$\rule{130}{2} \ Be \ Brainly\ \star$

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