Question

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

Answer 1

Step-by-step explanation:

Let Asha's age be X,

And Nieha's age be Y.

Therefore, X = 2+ Y^2 ------(i)

and, When Y becomes equal to X

then ,10* (Y+X) -1 = 2X

or, 10Y +10X -1 = 2X

or, 8X = 1- 10Y

or, X = (1-10Y)/8 ----------(ii)

From eq (i) and (ii) , we get ,

1-10Y = 16 + 8(Y^2)

8Y^2 +10Y + 15 = 0

Solve This you will get the answer....

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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