Question

(Exemplar)
Example 31. 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. Let the present age of Asha be x years and the present age of Nisha be y years,
mars​

Answer 1

Answer:

Nisha = 5 years old

Asha = 27 years old

Step-by-step explanation:

Let Nisha's age be x and Asha's age be y

1st Case

When Nisha is x years her mother is x² + 2 years that is

y = x² + 2

2nd Case

When Nisha grows to her mothers age

No. of years passed by = y - x

we know, y = x² + 2

so, No. of years passed by = (x² + 2 - x)

So, after x² + 2 - x years

Nisha's will be x + (x² + 2 - x) = x² + 2 (That is logical because she is reaching her mothers age)

Then,

Asha's age will be x² + 2 + (x² + 2 - x)

= 2x² + 4 - x

Now According to the Question

2x² - x + 4 = 10x - 1

2x² - x + 4 - 10x + 1 = 0

2x² - 11x + 5 = 0

ax² + bx + c = 0

Using Splitting the middle term method

Sum = b = -11

Product = (a × c) = 10

Thus, factors are -10 and -1

2x² - 10x - x + 5 = 0

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

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

Solving for x we get

so, x = 5 or x = 1/2

If we say Nisha is 1/2 years old then Mothers age would be 2.25 years which is not possible so x = 5

Now,

Asha's age = y

y = x² + 2

= 5² + 2

= 25 + 2 = 27

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

Hope you understood it........All the best