Question

A person on tour has rupees $4200$ for his expenses. If he extends his tour for $3$ days, he has to cut down daily expenses by rupees $70$. Find the original duration of the tour.

Answer 1

Total money $=4200$

Let tour days $=x$

Expense per day $=\frac{4200}{x}$

tour extended to $x+3$ days

Expense per day $=\frac{4200}{x+3}$

$\frac{4200}{x}=\frac{4200}{x+3}+70$

$\frac{4200}{x}=\frac{4200+70x+210}{x+3}$

$4200x+12600=4200x+70x^2+210x$

$70x^2+210x-12600=0$

$x^2+3x-180=0$

$x^2+15x-12x-180=0$

$(x+15)(x-12)=0$

so $x=12$ days