Question

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

Answer 1

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

Total expenditure on tour $=Rs.360$

Expenditure per day $=Rs.\frac{360}{x}$

Duration of the extended tour $=(x+4)$ days
Expenditure per day according to new schedule $=Rs.\frac{360}{x+4}$

It is given that the daily expenses are cut down by Rs. $3$

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

$\Rightarrow \frac{360(x+4)-360x}{x(x+4)}=3\Rightarrow \frac{360x+1440-360x}{x(x+4)}=3$

$\Rightarrow \frac{1440}{x^2+4x}=3\Rightarrow x^2+4x=480\Rightarrow x^2+4x-480=0$

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

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

$\Rightarrow x-20=0orx+24=0\Rightarrow x=20,x=-24$

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

Hence, the original duration of the tour was $20$ days.