Question

Hey $\large{\red{\underline{\sf{\orange{\pmb{MATHEMATICS \: \: \: WIZARD}}}}}}$ !

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.
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Answer 1

Answer :-

Let the present age of Nisha be x

Asha's age = x² + 2

Now, when the Nisha will turn into her mother's age, her age would be x² + 2

Asha's age would be 10x - 1

Now, we have to calculate the number of years that have been passed by Nisha and Asha and then we will equate them.

Years passed by Nisha = x² + 2 - x

Years passed by Asha = 10x - 1 - ( x² + 2 )

Years passed by Nisha = Years passed by Asha

→ x² + 2 - x = 10x - 1 - ( x² + 2 )

→ x² + 2 - x = 10x - 1 - x² - 2

→ x² + 2 - x - ( 10x - 1 - x² - 2 ) = 0

→ x² + 2 - x - 10x + 1 + x² + 2 = 0

→ x² + x² - x - 10x + 2 + 1 + 2 = 0

→ 2x² - 11x + 5 = 0

→ 2x² - 10x - x + 5 = 0

→ 2x ( x - 5 ) - 1 ( x - 5 ) = 0

→ ( 2x - 1 ) ( x - 5 ) = 0

→ x = ½ , 5

Now, ½ year is not possible, so the value of x = 5.

Present age of Nisha = 5 years

Present age of Asha = 5² + 2 = 27 years

Answer 2

A N S W E R :

• Present age of Nisha is 5 years.

• Present age of Asha is x² + 2 = (5)² + 2 = 25 + 2 = 27 years.

Given :

• Present Asha's age (in years) is 2 more than the square of her daughter Nisha's age

• Nisha grows to her mother's present age, Asha age would be one year less than 10 times the present age of Nisha

To find :

• Find the Present age of both Asha and Nisha ?

Solution :

• 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

lgnoring, x = 1/2 because then Asha's age = x² + 2 = which is not possible

Hence,

• Present age of Nisha = 5 years

• Present age of Asha is x² + 2 = (5)² + 2 = 25 + 2 = 27 years.