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
Solution:
Given, at present Asha’s age is 2 more than the square of her daughter Nisha’s age.
Also, when Nisha grows to her mother’s present age, Asha’s age will be one year less than 10 times the present age of Nisha.
We have to find the present age of both Asha and Nisha.
Let the age of Nisha be x.
Then, Asha’s age = x² + 2
As per given condition,
(x² + 2) + [(x² + 2) - x] = 10x - 1
2x² + 4 - x - 10x + 1 = 0
2x² - 11x + 5 = 0
On factoring,
2x² + 10x - x + 5 = 0
2x(x + 5) - 1(x - 5) = 0
(2x - 1)(x - 5) = 0
Now, 2x - 1 = 0
2x = 1
x = 1/2
Also, x - 5 = 0
x = 5
Age of Nisha = 1/2 years is not possible.
So, the age of Nisha = 5 years.
Age of Asha = (5)² + 2 = 25 + 2 = 27 years.
Therefore, the present ages of Nisha and Asha are 5 years and 27 years.
✦ Try This: At present Asha’s age (in years) is 3 l3ss 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 14 times the present age of Nisha. Find the present ages of both Asha and Nisha
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.4 Problem 6
At present Suma’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
Summary:
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. The present ages of both Nisha and Asha are 5 years and 27 years respectively.
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