Question

At present Asha s age (in years) is 2 more than the square of her daughter Nisha s age. WheNisha grows to her mother s present age, Asha s age would be one year less than 10 times thepresent age of Nisha. If present age of daughter Nisha be x years, then
(I) The present age of Asha is :
(A) 10x yrs (B) 2x²yrs
(C) (x²+2) yrs (D) x yrs

(ii) When Nisha grows to her mother s present age, then her mother s age is
(A)(x²+2) yrs (B)(2x²-x+4)yrs
(C)(x²+10)yrs (D)(x²+x+2) yrs

(iii) The quadratic equation formed is :
(A) x²-11x+5=0
(B) 2x²+11x-5=0
(C) 2x²+11x+5=0
(D) 2x²-11x+5=0

(iv) The present ages of Nisha and Asha are respectively
(A) 27 yrs, 5 yrs
(B) 10 yrs, 20 yrs
(C) 5 yrs, 27 yrs
(D) 5 yrs, 25 yrs​

Answer 1

Answer:

I)Correct option is

A

32

Let nisha's present age be x,

Asha's present age =x

2

+2

When Nisha turns her mother's age, x

2

+2−x years have passed. Asha's age =10x−1

⇒x

2+2−x = 10x−1−[x 2+2]

⇒2x

2

−11x+5=0

⇒(x−5)∗(2x+1)=0

⇒(x−5)=0 or (2x+1)=0

⇒x=5 or x=

2

−1

Since age can not be negative,

x=5 is the right answer.

Nisha's age is 5, Asha's age is 27

Sum of their present ages =5+27=32