Question

Asha's age is 2 more than the square of nisha's age.wen nisha grows to asha's present age,asha would be 1 year less than10 times the present age of nisha.find their ages

Answer 1

Let Nisha's age is x years Aisha's age = (x² + 2) years 
Now, A/C 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 = 0x = 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 

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