Question

At present Asha's age 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 1 year less than 10 times present age of Nisha.
Find their present ages.

Answer 1

Answer:

Let Asha,s age be x and her daughter's age be y.

Now,

x=2+y^2

Again,

10y-1=x+(x-y)

10y-1=2x-y

11y-1=2x

11y-1=2(2+y^2)

11y-1=4+2y^2

2y^2-11y+4+1=0

2y^2-11y+5=0

2y^2-10y-y+5=0

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

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

Either,                                  or,

y-5=0                                    2y-1=0

y=5                                  y=1/2(It is not a solution)\

x=2+y^2=2+5^2=27

Therefore, the age of Asha is 27 and of her daughter is 5.

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