Question

A person on tour has$₹360$ for his expenses. If he extends his tour for $4$ days, he has to cut down his daily expenses by $₹3$. Find the original duration of the tour.

Answer 1

Let $x$ days be the original duration of the tour.

Total expenditure on tour $=₹360$

Expenditure per day $=\frac{₹360}{x}$

Duration of the extended tour $=(x+4)$ days

Expenditure per day according to the new schedule$=\frac{₹360}{x+4}$

Given that daily expenses are cut down by $₹3$

As per the given condition

$\frac{360}{x}-\frac{360}{x+4}=3$

$\Rightarrow 360\left(\frac{1}{x}-\frac{1}{x+4}\right)=3$

$\Rightarrow \left(\frac{1}{x}-\frac{1}{x+4}\right)=\frac{3}{360}$

$\Rightarrow \frac{x+4-x}{x\left(x+4\right)}=\frac{1}{120}$

$\Rightarrow \frac{4}{x\left(x+4\right)}=\frac{1}{120}$

$\Rightarrow x\left(x+4\right)=480$

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

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

$\Rightarrow x^2+24x–20x–480=0$

$\Rightarrow x(x+24)–20(x+24)=0$

$\Rightarrow x–20=0orx+24=0$

$\Rightarrow x=20orx=-24$

Since the number of days cannot be negative. So, $x=20$

Therefore, the original duration of the tour was $20$ days