Question

at present asha's age is 2 more than the square of her daughter nisha's age. when nisha grows to her mothers present age asha's age would be one year less than 10 times the present age of nisha. find their present ages​

Answer 1

let Nisha's age be x ... so Asha's age will be x2 + 2

difference in asha's and nisha's ages = x2 + 2 - x

now...it is given " when nisha grows to her mother's age " so , after x2 + 2 - x years....nisha will grow to asha's age...!!

now to calculate asha's age when nisha's age will be x2 + 2 , we will add x2 +2 to x2 + 2 - x ...!!

i.e. x2 + 2 + x2 + 2 - x = 10x -1

2x2 + 4 - x = 10x - 1

2x2 - 11x + 5 = 0

2x2 - 10x - 1x + 5 = 0

2x ( x -5 ) -1 ( x - 5) = 0

(2x - 1) ( x - 5 ) = 0

so , x = 5 years....which is nisha's age

finally, asha's age = x2 + 2 = 27

Hopes this helps u..!! :)

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