Question

A certain number of men went to a hotel. Each man spent as many Rupees as one fourth of the men . If the total bill paid was Rupees 20449 then how many men visited the hotel ???​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The number of men visited the hotel is 286.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Each man spends = $\sf{\dfrac{1}{4}}$ of the men

Total money paid = Rs. 20499

To find :

Number of men visited the hotel

Solution :

Consider the number of men as y

Each man spent = $\sf{\dfrac{1}{4}y}$

★ Equation : $\boxed{\sf{y \times \frac{1}{4}y}=20449}$

$\sf{\implies} \: y \times \dfrac{1}{4}y = 20449$

$\sf{\implies} \: y \times y = 20449 \times 4$

$\sf{\implies} \: {y}^{2} =81796$

$\sf{\implies} \: y = \sqrt{81796}$

$\sf{\implies} \: y = 286$

$\therefore$ The number of men visited the hotel is 286.

Answer 2

Quadratic Equations :

Solution :

Let the number of men visited the hotel be x.

Each men spent as many rupees as one fourth ( 1/4 ) of the men = x * ( x/4 )

According to the question,

$\boxed{\mathsf{\green{x\:{\times{\dfrac{x}{4}\:=\:20449}}}}}$

$\mathsf{{x} ^{2}\:=\:20449\:{\times{4}}}$

$\mathsf{{x} ^{2}\:=\:81796}$

$\mathsf{x\:=\:{\sqrt{81796}}}$

$\mathsf{x\:=\:{\sqrt{2*2*11*11*13*13}}}$

$\mathsf{x\:=\:2*11*13}$

$\mathsf{x\:=\:286}$

⛛ Number of men visited the hotel = 286.