Question

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

hello....

Present age of Asha is 2+x2 yrs

Present age of Nisha is x yrs.

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

 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 , 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

asha 's age = x2 + 2 = 27

thank you...

☺

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