Question

The students of a class arranged a picnic. Each student contributed as many rupees as the
number of students in the class. If the total contribution is Rs 1156, find the strength of the class.​

Answer 1

Answer :-

$\: \: \underline{\boxed{\bf{\mapsto \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Quadratic Equations has been used. We know that, if the equation contains any varible term with the power of 2, then ut might be regarded as Quadratic Equation. Here we can formulate the equation according to the question, and then find our answer. Let's do that !

_____________________________________________

★ Question :-

The students of a class arranged a picnic. Each student contributed as many rupees as the number of students in the class. If the total contribution is Rs 1156, find the strength of the class.

______________________________________________

★ Solution :-

Given,

» Each student contributed as many rupees as the number of students in the class.

» Total money collected = Rs. 1156

• Let the number of student in the class be 'x', then,

» Number of students in class = Money paid by each student = x

Now according to the question,

⌬ Number of Students × Money Paid by each student = Total money collected.

⌬ x × x = 1156

⌬ x² = 1156

$\: \: \huge{\bf{\longrightarrow \: \: x \: = \: \sqrt{1156} \: = \: 34}}$

$\: \: \huge{\boxed{\bf{\Longrightarrow \: \: x = 34}}}$

• Hence, the number of students and money paid by each student = x = 34

$\: \: \underline{\boxed{\bf{\mapsto \: \: Thus, \: the \: number \: of \: students \: in \: the \: class \: are \: \underline{34} \: and \: money \: paid \: by \: each \: student \: is \: \underline{Rs.\: 34}}}}$

_______________________________________

$\: \: \underline{\boxed{\sf{\mapsto \: \: Confused? \: Don't \: worry \: let's \: verify \: it}}}$

For verification we need to simply apply the values, we got, into the equation we formed. Then,

⌬ x² = 1156

⌬ (34)² = 1156

⌬ 34 × 34 = 1156

⌬ 1156 = 1156

Here, the condition satisfies. So our answer is correct.

Hence, Verified.

_______________________________________

$\: \: \underline{\boxed{\tt{\mapsto \: \: Let's \: understand \: more}}}$

• Quadratic Equations are the equation formed by constant and variable terms that have standard form to be ax² + bx + c = 0. Here the highest degree is 2 which gives 2 solution of the equation that is two values of x.

• Polynomials are the equations formed using constant and variable terms and can have many different degrees. Different forms of Polynomials are :-

• Linear Polynomial
• Quadratic Polynomial
• Cubic Polynomial
• Bi - Quadratic Polynomial

Answer 2

Given :

• Each student contributed as many rupees as the number of students
• Total contribution = Rs. 1156

To find :

• Strength of cIass

SoIution :

Let the total strength of class or total number of students be N

∴ Contribution from 1 student = Rs. N

∴ Contribution from N students = N * N = N²

Now atq,

⇒ N * N = 1156

⇒ N² = 1156

⇒ N = √1156

⇒ N = 34

Therefore,

Total strength of class = 34

_________________________________

Verification :

If totaI strength of cIass is 34 then,

∴ Each student contributed = Rs. 34

∴ 34 students contributed = Rs. 34 * 34

                                             = Rs. 1156

∴ LHS = RHS              [Verified]