Answer
398.4k+ views
Hint: To solve this question first let us assume the number of students to be x. then as given in the question every student of a class sends a card to every other student. So each student sends a card to $n-1$ students. By equating the obtained equation to 600 and simplifying the obtained equation we get the desired answer.
Complete step by step answer:
We have been given that on a New Year day every student of a class sends a card to every other student and the postman delivers 600 cards.
We have to find the number of students in the class.
Let the number of students in the class is n.
Now, as given in the question that every student of a class sends a card to every other student it means each student sends a card to $n-1$ students.
The postman delivers 600 cards. Then we will get
$\Rightarrow n\left( n-1 \right)=600$
Simplifying the above equation we will get
$\begin{align}
& \Rightarrow {{n}^{2}}-n=600 \\
& \Rightarrow {{n}^{2}}-n-600=0 \\
\end{align}$
The above obtained equation is a quadratic equation. So we will solve the equation by splitting the middle term. Then we will get
$\begin{align}
& \Rightarrow {{n}^{2}}-\left( 25n-24n \right)-600=0 \\
& \Rightarrow {{n}^{2}}-25n+24n-600=0 \\
\end{align}$
Now, taking the common terms out we will get
$\Rightarrow n\left( n-25 \right)+24\left( n-25 \right)=0$
Now, again taking common terms out we will get
$\Rightarrow \left( n-25 \right)\left( n+24 \right)=0$
Now, equating each factor to zero we will get
$\Rightarrow \left( n-25 \right)=0$ and $\left( n+24 \right)=0$
Simplifying both we will get
$\Rightarrow n=25$ and $n=-24$
As n is the number of students so it can’t take negative value. So we ignore the negative value. The number of students in the class is 25.
So, option C is correct.
Note: Students can give the correct answer as 24 by ignoring the sign, which is incorrect. Students can solve the obtained quadratic equation by using the quadratic formula which is given as $x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ . By comparing the equation with the general equation students easily get the values of a, b and c.
Complete step by step answer:
We have been given that on a New Year day every student of a class sends a card to every other student and the postman delivers 600 cards.
We have to find the number of students in the class.
Let the number of students in the class is n.
Now, as given in the question that every student of a class sends a card to every other student it means each student sends a card to $n-1$ students.
The postman delivers 600 cards. Then we will get
$\Rightarrow n\left( n-1 \right)=600$
Simplifying the above equation we will get
$\begin{align}
& \Rightarrow {{n}^{2}}-n=600 \\
& \Rightarrow {{n}^{2}}-n-600=0 \\
\end{align}$
The above obtained equation is a quadratic equation. So we will solve the equation by splitting the middle term. Then we will get
$\begin{align}
& \Rightarrow {{n}^{2}}-\left( 25n-24n \right)-600=0 \\
& \Rightarrow {{n}^{2}}-25n+24n-600=0 \\
\end{align}$
Now, taking the common terms out we will get
$\Rightarrow n\left( n-25 \right)+24\left( n-25 \right)=0$
Now, again taking common terms out we will get
$\Rightarrow \left( n-25 \right)\left( n+24 \right)=0$
Now, equating each factor to zero we will get
$\Rightarrow \left( n-25 \right)=0$ and $\left( n+24 \right)=0$
Simplifying both we will get
$\Rightarrow n=25$ and $n=-24$
As n is the number of students so it can’t take negative value. So we ignore the negative value. The number of students in the class is 25.
So, option C is correct.
Note: Students can give the correct answer as 24 by ignoring the sign, which is incorrect. Students can solve the obtained quadratic equation by using the quadratic formula which is given as $x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ . By comparing the equation with the general equation students easily get the values of a, b and c.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)