A person on tour has ₹10800 for his expenses. If he extends his tour by 4 days, he has to cut down his daily expenses by ₹90.

Let the original duration of the tour be x days.

$\therefore$ Original daily expenses $=₹ \frac{10,800}{x}$

If he extends his tour by 4 days, then his new daily expenses $=₹ \frac{10,800}{x+4}$

According to the given condition,

$₹ \frac{10,800}{x}-₹ \frac{10,800}{x+4}=₹ 90$

$\Rightarrow \frac{10800 x+43200-10800 x}{x(x+4)}=90$

$\Rightarrow \frac{43200}{x^{2}+4 x}=90$

$\Rightarrow x^{2}+4 x=480$

$\Rightarrow x^{2}+4 x-480=0$

$\Rightarrow x^{2}+24 x-20 x-480=0$

$\Rightarrow x(x+24)-20(x+24)=0$

$\Rightarrow(x+24)(x-20)=0$

$\Rightarrow x+24=0$ or $x-20=0$

$\Rightarrow x=-24$ or $x=20$

∴ x = 20              (Number of days cannot be negative)

Hence, the original duration of the tour is 20 days.