Question

at present madhuri age is 2 more thane the square of her daughter nayana's age. when nayana grows to her mother's present age. madhuri's age would be one year less than the 10 times the present age of nayana. find the present age of both

Answer 1

Step-by-step explanation:

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Answer 2

Present age of Nayana is 5 years and Madhuri's age is 27 years.

Step-by-step explanation:

Let the present age of Nayana = x

Her mother Madhuri's present age = x² + 2

When Nayana grows to her mother's present age, Madhuri's age would be one year less than 10 times the present age of Nayana.

Nayana's age when she grows to her mother's present age = x² + 2

Number of years between Nayana's present age and her mother's age = [(x² + 2)-x]

Therefore, Madhuri's present age after  [(x² + 2)-x] years = x² + 2 +(x² + 2 - x)

Now the equation will be :

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

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

2x - 1 = 0 ⇒ x = $\frac{1}{2}$

and x - 5 = 0 ⇒ x = 5

Present age of Nayana = 5 years

and age of Madhuri = 5²+2 = 27 years

x = $\frac{1}{2}$ can not be the answer because then the Madhuri's age will be $2\frac{1}{4}$ years  which is not possible.

Therefore, present age of Nayana is 5 years and Madhuri's age is 27 years.

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