Let Mr. Arun is on tour for x days

Then, According to the question

Difference in expenses per day and extended tour is 

$$\begin{gathered} = \frac{360}{x}-\frac{360}{\left(x+4\right)}=3 \\ =360 \left(\frac{1}{x}-\frac{1}{\left(x+4\right)}\right)=3 \\ =\left(\frac{1}{x}-\frac{1}{\left(x+4\right)}\right)=\frac{3}{360} \\ =\left(\frac{1}{x}-\frac{1}{\left(x+4\right)}\right)=\frac{1}{120} \\ =\left(\frac{x+4-x}{x\left(x+4\right)}\right)=\frac{1}{120} \\ =\left(\frac{4}{x^2+4x}\right)=\frac{1}{120} \\ =x^2+4x=4\times 120 \\ =x^2+4x=480 \\ =x^2+4x-480=0 \\ =x^2+24x-20x-480=0 \\ =\left(x+4\right) \left(x-20\right)=0 \\ \therefore x=20 \end{gathered}$$

(We ignore the '-ve' value of 'x')

i.e, Because day's cannot be negative.