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Q2(iii):
Represent the following situations in the form of quadratic equations : (iii) Rohan’s mother is $26$ years older than him. The product of their ages (in years) $3$ years from now will be $360$. We would like to find Rohan’s present age.

Solution :

Given:

1. Rohan’s mother is $26$ years older than Rohan.

2. The product of their ages $3$ years from now will be $360$.

To Find:

Represent the given situation in the form of a quadratic equation in terms of Rohan's present age.

Step 1: Defining the Variables

Let the present age of Rohan be $x$ years.

Since Rohan’s mother is $26$ years older than him, the present age of Rohan’s mother is $(x + 26)$ years.

Step 2: Determining Ages 3 Years from Now

After $3$ years, the age of each person will increase by $3$ years.

Rohan’s age after $3$ years = $(x + 3)$ years.

Rohan’s mother’s age after $3$ years = $(x + 26) + 3 = (x + 29)$ years.

Step 3: Formulating the Equation

According to the problem, the product of their ages $3$ years from now is $360$.

Therefore, we set up the equation:

$(x + 3)(x + 29) = 360$

Step 4: Expanding and Simplifying the Equation

Using the distributive property (FOIL method) to expand the left side:

$x(x + 29) + 3(x + 29) = 360$

$x^2 + 29x + 3x + 87 = 360$

[Combining like terms $29x$ and $3x$]:

$x^2 + 32x + 87 = 360$

Step 5: Bringing the Equation to Standard Form

The standard form of a quadratic equation is $ax^2 + bx + c = 0$. Subtract $360$ from both sides:

$x^2 + 32x + 87 - 360 = 0$

$x^2 + 32x - 273 = 0$

Justification:

The resulting equation $x^2 + 32x - 273 = 0$ is a polynomial of degree $2$, which satisfies the definition of a quadratic equation where $a=1$, $b=32$, and $c=-273$.

Final Answer: The quadratic equation representing the situation is $x^2 + 32x - 273 = 0$, where $x$ is Rohan's present age.


More Questions from Class 10 Mathematics Quadratic Equations EXERCISE 4.1


CBSE Solutions for Class 10 Mathematics Quadratic Equations


Chapters in CBSE - Class 10 Mathematics


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I started my teaching career in 2005 in that year itself I got a chance to take class in 10 for one month for leave vacancy. After that I got the chance in 2011 in another school, then it continued. Taking class in 10 it was a challenge because responsibilities are more. Both parents and students are in stress, at the same time the school management also. If the results are not satisfactory it will affect to the reputation of the school. So the teachers are alert always .All the students have to face the board. So the preparation of each and every child is important. For that conducting special classes ,morning classes. Conducting evaluations in proper interval. After every evaluation a session with parents in school is very important. Because they are more stressed than students. The year tenth is important because it is the turning point of each student . The effort of all the pupils will be fruitful when we get the good result. Teachers especially those who are taking in class 10 they are not bothered about the salary which the management as paying to them, of course it is a pain to their personal life. Once if we are standing in front of the students our main attention was that whether the concept will be reaching to the pupil in the right meaning and sense. In that time we are not bothered about the payment. If the student got the concept and scored good in exam that was the great reward for teacher. After the schooling that student and parents never forget that teacher in their life every important movements they expect that teachers presence there.

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