Question

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. Find the original duration of the tour.

Answer 1

Let the original duration of the tour be x days.

∴ 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

$$\begin{gathered} \Rightarrow \frac{10800x+43200-10800x}{x\left(x+4\right)}=90 \\ \Rightarrow \frac{43200}{x^2+4x}=90 \\ \Rightarrow x^2+4x=480 \\ \Rightarrow x^2+4x-480=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow x^2+24x-20x-480=0 \\ \Rightarrow x\left(x+24\right)-20\left(x+24\right)=0 \\ \Rightarrow \left(x+24\right)\left(x-20\right)=0 \\ \Rightarrow x+24=0\mathrm{or}x-20=0 \end{gathered}$$
$\Rightarrow x=-24\mathrm{or}x=20$
∴ x = 20 (Number of days cannot be negative)

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