The hotel bill for a number of people for overnight stay is ₹4800 . If there were 4 more the bill each person had to pay would have reduced by ₹200. Find the number of people staying overnight.

Let the number of people be x

Total bill = ₹4800

∴ Bill amount each person has to pay = $\dfrac{4800}{x}$

If there were 4 more people then bill each has to pay = $\dfrac{4800}{x + 4}$

According to question,

$\Rightarrow \dfrac{4800}{x} - \dfrac{4800}{x + 4} = 200 \\[1em] \Rightarrow \dfrac{4800(x + 4) - 4800x}{x(x + 4)} = 200 \\[1em] \Rightarrow 4800x - 4800x + 19200 = 200x(x + 4) \\[1em] \Rightarrow 19200 = 200x^2 + 800x \\[1em] \Rightarrow 200x^2 + 800x - 19200 = 0 \\[1em] \Rightarrow x^2 + 4x - 96 = 0 \text{ (On Dividing the equation by 200) } \\[1em] \Rightarrow x^2 + 12x - 8x - 96 = 0 \\[1em] \Rightarrow x(x + 12) - 8(x + 12) = 0 \\[1em] \Rightarrow (x - 8)(x + 12) = 0 \\[1em] x = 8 \text{ or } x = -12$

Since, number of people cannot be negative hence, x ≠ -12

∴ x = 8

Hence, the number of people staying overnight are 8.