Question

A certain number of men went to a hotel. Each man spent as much as many rupees as one-fourth of the men. If the total bill paid was Rs.20,449, then how many men visited the hotel?

Answer 1

Hint: First we take a variable as the number of men went to a hotel.
The total amount of the bill paid is given, then applying the condition we will get one equation.
By solving the equations we will get the number of men who went to the hotel.

Complete step by step answer:
It is given that, a certain number of men went to a hotel & each man spent as much as many rupees as one-fourth of the men.
Also, the total bill paid by all of them was Rs 20449.
Let, the number of men who went to a hotel be denoted by the variable be $x$.
The amount each man spent given by the condition is that Rs.\[\dfrac{1}{4} \times x\]
Hence by the given condition we can come to a conclusion that the total bill amount is Rs. \[x \times \dfrac{x}{4}\].
Now we equate the above value with the given total bill amount we get,
\[x \times \dfrac{x}{4} = 20449\]
Which in turn implies that
\[\dfrac{{{x^2}}}{4} = 20449\]
Let us multiply by 4 on both sides we get,
\[{x^2} = 20449 \times 4\]
Let us take square root on both sides we get,
\[x = \sqrt {81796} \]
That is \[x = 286\]

Hence the number of men who went to a hotel is 286.

Note:
In these kinds of questions, clearly understand the logic among the given values and form equations. If we get one equation with one variable, we can solve it easily. Here we have taken the total number of men as the only one variable hence we have solved it easily.