Question

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

Answer 1

Answer: Prisha's present age is 7 years and Nisha's present age is 48 years.

Step-by-step explanation:

Let,

Prisha's present age= X years

Nisha's present age= Y years

From the question we get,

Y= X^2 +2.......(a)

and, Y= 10X -1.......(b)

Using the value of Y and putting it in equation (a),

10X -1 = X^2 +2

or, X^2-10X= -3

or, X(X-10)= -3

So, Either, X= -3

or, X-10= -3

or, X=7

Age cannot be negative. So, Prisha's present age is 7 years.

Putting the value of X in (a),

Y= 49 -1

or, Y= 48

So, Nisha's present age is 48 years.

Answer 2

Answer: The present age of Prisha is 5 years and Nisha is 27 years.

Step-by-step explanation:

Let, the present age of Prisha be ‘x’.  

Therefore, the present age of Nisha is x² + 2.

Now, the number of years after which Prisha will be of her Mother’s (Nisha) age = (x²+2) -x

Hence, Nisha’s age at the same time will be = (x²+2) + {(x²+2) -x}

Also, given that, at the same time Nisha’s Age will be 1 year less than present age of Prisha, i.e. (10x -1)

Hence, according to the question:

(x²+2) + {(x²+2) -x} = 10x – 1

Or, x² + 2 + {x² + 2 -x } = 10x -1

Or, 2x² + 4 -x = 10x -1

Or, 2x² + 4 -x -10x + 1 = 0

Or, 2x² -10x -x + 5 = 0

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

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

Hence, x = 5 or x= ½

Since, age cannot be in fraction.

Hence the current age of Prisha is 5 years  and the Present age of Nisha is (5² + 2) = 27 years.