Question

"A hotel bill for a number of people for overnight stay is Rs.4800. If there were 4 more people, the bill each person had to pay, would have reduced by Rs.200. Find the number of people staying overnight."
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Answer 1

Answer:

Correct option is

B

8

Let the number of people staying overnight be x.

For x people, the hotel bill =Rs.4800

For 1 person, the hotel bill = x4800

When 4 people were more, the hotel bill = x+44800

The bill paid by each person is reduced by Rs.200.

Therefore, x4800−x+44800=200

x(x+4)4800(x+4)−4800x=200

4800x+19200−4800x=x2+4x=20019200=96

x2+4x−96=0

Using 2a−b±b2−4ac to find the roots of the equation

⇒x=2×1−4±(4)2−4×1×(−96)

⇒x=2−4±400

⇒

hope its helpful

Answer 2

$\large\underline{\sf{Solution-}}$

Let number of people staying overnight be 'x'.

According to statement,

A hotel bill of 'x' number of people for overnight stay is Rs 4800.

So,

$\rm :\longmapsto\:Each \: person \: share \: = \: Rs \: \dfrac{4800}{x} - - - (1)$

According to statement again,

Number of persons increased by 4.

So,

Total number of persons = x + 4

A hotel bill of 'x + 4' number of people for overnight stay is Rs 4800.

Thus,

$\rm :\longmapsto\:Each \: person \: share \: = \: Rs \: \dfrac{4800}{x + 4} - - - (2)$

According to statement again,

$\rm :\longmapsto\:\dfrac{4800}{x} - \dfrac{4800}{x + 4} = 200$

$\rm :\longmapsto\:4800\bigg(\dfrac{1}{x} - \dfrac{1}{x + 4} \bigg) = 200$

$\rm :\longmapsto\:2400\bigg(\dfrac{x + 4 - x}{x(x + 4)} \bigg) = 1$

$\rm :\longmapsto\:2400\bigg(\dfrac{4}{x(x + 4)} \bigg) = 1$

$\rm :\longmapsto\:\bigg(\dfrac{9600}{x(x + 4)} \bigg) = 1$

$\rm :\longmapsto\: {x}^{2} + 4x = 9600$

$\rm :\longmapsto\: {x}^{2} + 4x - 9600 = 0$

$\rm :\longmapsto\: {x}^{2} + 100x - 96x - 9600 = 0$

$\rm :\longmapsto\:x(x + 100) - 96(x + 100) = 0$

$\rm :\longmapsto\:(x - 96)(x + 100) = 0$

$\rm :\implies\:x = 96 \: \: \: \: or \: \: \: \: - 100 \: \: \: \{rejected \}$

$\rm \implies\:x = 96$

Hence,

• Number of people staying overnight is 96.

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.