Question

at present nisha s age (in years) is 2 more than the square of her daughter Nisha s age when nisha 's grows to her mothers present age ,Asha's age wpuld be one year less than 10 times the present age of Nisha. find the present age of both asha and nisha

Answer 1

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