Answer
Verified
480.3k+ views
Hint:- Let us write equations for the given conditions and then find the age of Nisha and her mother by solving the equations.
Complete step-by-step answer:
Let the present age of Asha will be x years.
And the present age of Nisha will be y years.
So, according to the present age condition given for Nisha and her mother.
Square of Nisha present age will be y*y = \[{{\text{y}}^{\text{2}}}\].
So, Asha age will be 2 more than the square of Nisha age.
So, x = \[{{\text{y}}^{\text{2}}}\] + 2 (1)
And the difference in the ages of Nisha and her mother is (x – y) years.
As we know that difference in their present age is (x – y). So, after (x – y) years Nisha’s age will become equal to the present age of her mother.
So, after (x – y) years.
Nisha age will be y + (x – y) = x years.
And, Asha age will be x + (x – y) = 2x – y years.
And according to the question, when Nisha is the present age of her mother (x years) then Asha age would be one year less than 10 times the present age of Nisha.
So, Asha age will be (10y – 1) years.
But we had above found that Asha age would be (2x – y) years.
So, 2x – y = 10y – 1.
Now solving the above equation to get the value of x.
2x = 11y – 1
x = \[\dfrac{{{\text{11y - 1}}}}{{\text{2}}}\] (2)
Now putting the value of x in equation 1. We get,
\[\dfrac{{{\text{11y - 1}}}}{{\text{2}}}\] = \[{{\text{y}}^{\text{2}}}\] + 2
On, cross-multiplying above equation.
11y – 1 = 2\[{{\text{y}}^{\text{2}}}\] + 4
2\[{{\text{y}}^{\text{2}}}\] – 11y + 5 = 0 (3)
Now, we had to solve equation 3 to get the value of y.
On, splitting middle term 11y. We get,
2\[{{\text{y}}^{\text{2}}}\] – 10y – y + 5 = 0
Now making the factor of the above equation to get the value of y.
2y (y – 5) –1(y – 5) = 0
Taking (y – 5) common from the above equation. We get,
(y – 5)(2y – 1) = 0
From above equation y = 5 years or y = \[\dfrac{{\text{1}}}{{\text{2}}}\]years or 6 months (impossible because in months).
Now putting the value of y in equation 2. We get,
x = \[\dfrac{{{\text{11(5) - 1}}}}{{\text{2}}}\] = \[\dfrac{{{\text{54}}}}{{\text{2}}}\] = 27 years
Hence, the present age of Nisha is 5 years and the present of Asha is 27 years.
Note:- Whenever we come up with this type of problem then first, we assume that their present ages are x and y years. And after that we had to find the equations of their ages according to the given conditions in question. After that we will solve the given equations to get appropriate values of x and y. And if any of the equations is quadratic then we have to neglect impossible values of x and y.
Complete step-by-step answer:
Let the present age of Asha will be x years.
And the present age of Nisha will be y years.
So, according to the present age condition given for Nisha and her mother.
Square of Nisha present age will be y*y = \[{{\text{y}}^{\text{2}}}\].
So, Asha age will be 2 more than the square of Nisha age.
So, x = \[{{\text{y}}^{\text{2}}}\] + 2 (1)
And the difference in the ages of Nisha and her mother is (x – y) years.
As we know that difference in their present age is (x – y). So, after (x – y) years Nisha’s age will become equal to the present age of her mother.
So, after (x – y) years.
Nisha age will be y + (x – y) = x years.
And, Asha age will be x + (x – y) = 2x – y years.
And according to the question, when Nisha is the present age of her mother (x years) then Asha age would be one year less than 10 times the present age of Nisha.
So, Asha age will be (10y – 1) years.
But we had above found that Asha age would be (2x – y) years.
So, 2x – y = 10y – 1.
Now solving the above equation to get the value of x.
2x = 11y – 1
x = \[\dfrac{{{\text{11y - 1}}}}{{\text{2}}}\] (2)
Now putting the value of x in equation 1. We get,
\[\dfrac{{{\text{11y - 1}}}}{{\text{2}}}\] = \[{{\text{y}}^{\text{2}}}\] + 2
On, cross-multiplying above equation.
11y – 1 = 2\[{{\text{y}}^{\text{2}}}\] + 4
2\[{{\text{y}}^{\text{2}}}\] – 11y + 5 = 0 (3)
Now, we had to solve equation 3 to get the value of y.
On, splitting middle term 11y. We get,
2\[{{\text{y}}^{\text{2}}}\] – 10y – y + 5 = 0
Now making the factor of the above equation to get the value of y.
2y (y – 5) –1(y – 5) = 0
Taking (y – 5) common from the above equation. We get,
(y – 5)(2y – 1) = 0
From above equation y = 5 years or y = \[\dfrac{{\text{1}}}{{\text{2}}}\]years or 6 months (impossible because in months).
Now putting the value of y in equation 2. We get,
x = \[\dfrac{{{\text{11(5) - 1}}}}{{\text{2}}}\] = \[\dfrac{{{\text{54}}}}{{\text{2}}}\] = 27 years
Hence, the present age of Nisha is 5 years and the present of Asha is 27 years.
Note:- Whenever we come up with this type of problem then first, we assume that their present ages are x and y years. And after that we had to find the equations of their ages according to the given conditions in question. After that we will solve the given equations to get appropriate values of x and y. And if any of the equations is quadratic then we have to neglect impossible values of x and y.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE